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Longer titles found: Skew-symmetric matrix (view), Persymmetric matrix (view)

searching for Symmetric matrix 113 found (304 total)

alternate case: symmetric matrix

Parallel axis theorem (2,323 words) [view diff] exact match in snippet view article find links to article

position of particle Pi, i = 1, ..., n. Recall that [ri − S] is the skew-symmetric matrix that performs the cross product, [ r i − S ] y = ( r i − S ) × y ,

In mathematics, an EP matrix (or range-Hermitian matrix or RPN matrix) is a square matrix A whose range is equal to the range of its conjugate transpose

"A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one." It is built out of many elementary

{1+x^{2}}}} is Nash on R. the function which associates to a real symmetric matrix its i-th eigenvalue (in increasing order) is Nash on the open subset

{\displaystyle A^{T}J=JA} , where  J {\displaystyle J}   is the skew-symmetric matrix defined as: J = [ 0 I n − I n 0 ] {\displaystyle

( A , B ) {\displaystyle (A,B)} is completely controllable, then a symmetric matrix P and a vector Q satisfying A T P + P A = − Q Q T {\displaystyle A^{T}P+PA=-QQ^{T}}

In mathematics, a jacket matrix is a square symmetric matrix A = ( a i j ) {\displaystyle A=(a_{ij})} of order n if its entries are non-zero and real,

Note: the above algorithm can be transformed so to make only one symmetric matrix-vector multiplication in each iteration. By making a few substitutions

theorem holds in the following sense: if M {\displaystyle M} is a symmetric matrix and the Hadamard product M ∘ N {\displaystyle M\circ N} is positive

probability of a random symmetric matrix is exponentially small. The paper addresses a long-standing conjecture concerning symmetric matrix with entries in {

X {\displaystyle X} be an m × m {\displaystyle m\times m} complex symmetric matrix. Then the hypergeometric function of a matrix argument X {\displaystyle

{\displaystyle V} with orthonormal columns and a tridiagonal real symmetric matrix T = V ∗ A V {\displaystyle T=V^{*}AV} of size m × m {\displaystyle

convention and β i k {\displaystyle \beta _{ik}} is a positive definite symmetric matrix. Using the quasi-stationary equilibrium approximation, that is, assuming

vectors at p. Then the principal curvatures are the eigenvalues of the symmetric matrix [ I I i j ] = [ I I ( X 1 , X 1 ) I I ( X 1 , X 2 ) I I ( X 2 , X 1

Often the weights w i j {\displaystyle w_{ij}} are represented as a symmetric matrix W = [ w i j ] {\displaystyle W=[w_{ij}]} with zeros along the diagonal

\lambda _{2}} denotes the second largest eigenvalue of the semi-positive symmetric matrix S := ( ⟨ A α , B β ⟩ ) {\displaystyle S:=(\left\langle A^{\alpha }

degree-2 forms (quadratic forms), based on the eigenvalues of the symmetric matrix representing the quadratic form. X 2 + Y 2 − Z 2 = 0 {\displaystyle

Lancaster & Qian Ye (1991) "Variational and numerical methods for symmetric matrix pencils", Bulletin of the Australian Mathematical Society 43: 1 to

non-singular, and for G = (A + I)−1(A − I), there exists a positive definite symmetric matrix W such that W − GTWG is positive definite. Semipositivity and diagonal

the diagonal elements equal. It is possible to find a nonsingular symmetric matrix P such that P ′ P = P P = V {\displaystyle \mathbf {P} ^{\prime }\mathbf

}dt\right){\boldsymbol {R}}_{\text{old}}} for the skew-symmetric matrix [ω]×. The errors induced by finite time steps tend to increase the

continuous functions on M with aij = aji. Suppose that for all x in M, the symmetric matrix [aij] is positive-definite. If u is a nonconstant C2 function on M

( x ) {\displaystyle M(x)} is a positive semidefinite (and hence symmetric) matrix describing the system's irreversible behaviour. In addition to the

x} is a vector of nodes in the network and W {\displaystyle W} is a symmetric matrix describing their connectivity. The continuous time update is d x d

of individuals as points in geometric space. The Burt table is the symmetric matrix of all two-way cross-tabulations between the categorical variables

u,\nabla u)\;dx,} where A ( x ) {\displaystyle A(x)} is a positive symmetric matrix. The Euler-Lagrange equation of a Dirichlet form is a non-local analogue

Andrew H. (1953). "A note on the Capelli operators associated with a symmetric matrix". Proceedings of the Edinburgh Mathematical Society. Series 2. 9 (1):

using nested dissection to compute the Cholesky factorization of a (symmetric) matrix in parallel. A given sparse ( n × n ) {\displaystyle (n\times n)}

Its Applications, 1997. V. V. Goryunov, V. M. Zakalyukin, "Simple symmetric matrix singularities and the subgroups of Weyl groups Aμ, Dμ, Eμ", Mosc. Math

j , k = 1 , . . . , g {\displaystyle j,k=1,...,g} . We can form a symmetric matrix whose entries are ∫ b k ζ j {\displaystyle \int _{b_{k}}\zeta _{j}}

^{T}=\mathbf {L} ^{T}\mathbf {L} =\mathbf {I} } . We can define an anti-symmetric matrix with this, Ω ∗ = d L d t L T {\displaystyle \mathbf {\Omega } ^{*}={\frac

Gorenstein rings of codimension 3 in terms of the Pfaffians of a skew-symmetric matrix, by Buchsbaum and Eisenbud. In 2011, Miles Reid extended this structure

_{j}^{\dagger }/2}\left|\mathrm {MFT} \right\rangle } where Z is a symmetric matrix with | Z | ≤ 1 {\displaystyle |Z|\leq 1} and N = ⟨ M F T | R P A ⟩

\nu )} . Here X 1 / 2 {\displaystyle \mathbf {X} ^{1/2}} denotes the symmetric matrix square root of X {\displaystyle \mathbf {X} } , the parameters Ψ ,

026 Giuseppe Geymonat, Francoise Krasucki, Hodge decomposition for symmetric matrix fields and the elasticity complex in Lipschitz domains, COMMUNICATIONS

"Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems", J. Comput. Phys., 44 (1): 1–19, Bibcode:1981JCoPh

{\displaystyle f} . The main difference is that the Hessian matrix is a symmetric matrix, unlike the Jacobian when searching for zeroes. Most quasi-Newton methods

+ B ] , {\displaystyle [A]=[I-B]^{-1}[I+B],} where [B] is the skew-symmetric matrix constructed from Rodrigues' vector b = tan ⁡ ϕ 2 S , {\displaystyle

Proof Proof Every positive-semidefinite symmetric matrix M {\textstyle {\boldsymbol {M}}} has a positive-semidefinite symmetric square root M 1 / 2 {\textstyle

parametric integrals, and their derivatives; 5) the Pfaffian of a skew symmetric matrix (either finite or infinite dimensional) with entries similarly of polynomial

Levi-Civita connection, the connection forms are given by the unique skew-symmetric matrix of 1-forms ω {\displaystyle \omega } that is torsion-free, i.e., that

characterized by its probability density function as follows: Let X be a p × p symmetric matrix of random variables that is positive semi-definite. Let V be a (fixed)

and let W {\displaystyle W} be an n × n {\displaystyle n\times n} symmetric matrix with w i j = w j i {\displaystyle w_{ij}=w_{ji}} . After some algebraic

the Rayleigh quotient with respect to a matrix M. Theorem Let M be a symmetric matrix and let x be the non-zero vector that maximizes the Rayleigh quotient

connected, so that every neuron is connected to every other neuron using a symmetric matrix of weights W I J {\displaystyle W_{IJ}} , indices I {\displaystyle

eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace

enumerated set of data points, the similarity matrix may be defined as a symmetric matrix A {\displaystyle A} , where A i j ≥ 0 {\displaystyle A_{ij}\geq 0}

cell. AI interpretability, genomics, data dashboards Correlogram A symmetric matrix showing pairwise correlations, often with color intensity and signs

would be obtained by thinking of C 1 {\displaystyle C_{1}} as the 3×3 symmetric matrix which represents it. If C 1 {\displaystyle C_{1}} and C 2 {\displaystyle

{\displaystyle A_{\mu }} is an n × n {\displaystyle n\times n} skew-symmetric matrix. (See the article on the metric connection for additional articulation

vanishing locus of a quadratic polynomial coming from a non-singular symmetric matrix. We can then restrict our attention to curves on Y = P 1 × P 1 {\displaystyle

cell. AI interpretability, genomics, data dashboards Correlogram A symmetric matrix showing pairwise correlations, often with color intensity and signs

itself results in the Cartan matrix, usually denoted C; this is a symmetric matrix such that the entries in its j-th row are the multiplicities of the

{1}{2}}}{\left(e^{i\pi /4}{\sqrt {2\pi }}\right)}^{N}} for any positive-definite symmetric matrix A {\displaystyle A} . Suppose A is a symmetric positive-definite (hence

{\displaystyle u=-R^{-1}B^{T}Px} , where P ( t ) {\displaystyle P(t)} is a symmetric matrix and satisfies the continuous-time algebraic Riccati equation − P ˙

itself results in the Cartan matrix, usually denoted C; this is a symmetric matrix such that the entries in its j-th row are the multiplicities of the

is simply what are the distances of the characteristic values of a symmetric matrix with random coefficients. — Eugene Wigner, Results and theory of resonance

elastic membranes and on waves in elastic media. He introduced a 3 × 3 symmetric matrix of numbers that is now known as the Cauchy stress tensor. In elasticity

unknown scalars and obtain homogeneous equations, define the anti-symmetric matrix H = ( 0 − 1 1 0 ) {\displaystyle \mathbf {H} ={\begin{pmatrix}0&-1

\Sigma } also has a Wishart distribution.[citation needed] Let X be a symmetric matrix of real numbers given by X = [ A B B T C ] . {\displaystyle

equivalent definition is in matrix form. Let V {\displaystyle V} be a p×p symmetric matrix, one can rewrite the sparse PCA problem as max T r ( Σ V ) subject

metric tensor g in the minimum s0 of V gives the positive definite and symmetric matrix G = g(s0)−1. One can solve the two matrix problems L T F L = Φ a n

We can see that B B T {\displaystyle {\boldsymbol {BB^{T}}}} is a symmetric matrix, therefore, so is W c {\displaystyle {\boldsymbol {W}}_{c}} . We can

to this frame and the Levi-Civita connection is given by the skew-symmetric matrix of 1-forms ω i j = ( 0 − d θ d θ 0 ) {\displaystyle {\omega

}},} where ω is the angular velocity vector obtained from the skew symmetric matrix [ Ω ] = A ˙ A T , {\displaystyle [\Omega ]={\dot {A}}A^{\mathsf {T}}

{e} _{2},\cdots ,\mathbf {e} _{p}} , by eigendecomposition of a real symmetric matrix, the covariance matrix Σ {\displaystyle \mathbf {\Sigma } } can be

additional structure, such as being symmetric or irreducible. For a real symmetric matrix A ∈ R n × n {\displaystyle A\in \mathbb {R} ^{n\times n}} , the Gershgorin

to any number of dimensions by noting that n̂i n̂iT is simply the symmetric matrix with all eigenvalues unity except for a zero eigenvalue in the direction

We can see that C T C {\displaystyle {\boldsymbol {C^{T}C}}} is a symmetric matrix, therefore, so is W o {\displaystyle {\boldsymbol {W}}_{o}} . We can

_{i},\sigma _{l},\sigma _{k},\sigma _{j}\right),} we see that A is a symmetric matrix (i.e. it is diagonalisable by an orthogonal matrix). So we write A

c_{j}]} where D i j = D j i ≥ 0 {\displaystyle D_{ij}=D_{ji}\geq 0} is a symmetric matrix of coefficients that characterize the intensities of jumps. The free

[I_{R}]=-\sum _{i=1}^{n}m_{i}[r_{i}-R][r_{i}-R],} where [ri − R] is the skew-symmetric matrix constructed from the vector ri − R. For the analysis of robotic systems

T Q x {\displaystyle p(x)=x^{T}Qx} where Q {\displaystyle Q} is a symmetric matrix. Similarly, polynomials of degree ≤ 2d can be expressed as p ( x )

stress matrix is symmetric and that the product of a skew matrix and a symmetric matrix is zero. Now recap. We have shown through the above derivation that

{\displaystyle G^{-1}} , and for the properties of the inverse of a symmetric matrix, they're also symmetric (D.6). g i j g j k = δ k i {\displaystyle g^{ij}g_{jk}=\delta

also symmetric. Then there is exactly one positive semidefinite and symmetric matrix B such that A = B B {\displaystyle A=BB} . This unique matrix is called

{\partial ^{2}\varphi (x,t)}{\partial x_{i}\partial x_{j}}}.} The symmetric matrix of diffusion coefficients Dij should be positive definite. It is needed

clique problem. Hoffman's bound: Let W {\displaystyle W} be a real symmetric matrix such that W i , j = 0 {\displaystyle W_{i,j}=0} whenever ( i , j )

{\displaystyle f:{\mathcal {X}}\rightarrow \mathbb {R} ^{T}} is a symmetric matrix-valued function Γ : X × X → R T × T {\displaystyle \Gamma :{\mathcal

{w^{T}Bw}{w^{T}Aw}}} , where B ∈ R d × d {\displaystyle B\in R^{d\times d}} is a symmetric matrix and A ∈ R d × d {\displaystyle A\in R^{d\times d}} is a symmetric positive

0} where A ⪰ 0 {\displaystyle A\succeq 0} indicates that a square symmetric matrix A {\displaystyle A} is non-negative definite. Consequently, any given

{w^{T}Bw}{w^{T}Aw}}} , where B ∈ R d × d {\displaystyle B\in R^{d\times d}} is a symmetric matrix and A ∈ R d × d {\displaystyle A\in R^{d\times d}} is a symmetric positive

connected, so that every neuron is connected to every other neuron using a symmetric matrix of weights W I J {\displaystyle W_{IJ}} , indices I {\displaystyle

However eigenvectors w(j) and w(k) corresponding to eigenvalues of a symmetric matrix are orthogonal (if the eigenvalues are different), or can be orthogonalised

R({\hat {n}},\theta )=e^{M\theta }} where M {\displaystyle M} is a skew-symmetric matrix and θ {\displaystyle \theta } is angle of rotation, we can express

\theta ^{k}g_{jk}(\theta _{0})+\mathrm {O} (\Delta \theta ^{3})} . The symmetric matrix g j k {\displaystyle g_{jk}} is positive (semi) definite and is the

{\displaystyle H=\operatorname {Tr} (F)} . The Fradkin Tensor is a thus a symmetric matrix, and for an n {\displaystyle n} -dimensional harmonic oscillator has

Horn & Johnson (1985, p. 407). "matrices - Diagonalizing a Complex Symmetric Matrix". MathOverflow. Retrieved 2020-01-25. Schabauer, Hannes; Pacher, Christoph;

=\mathbf {M} \mathbf {C} {\boldsymbol {\Phi }},} where H is a 3N × 3N symmetric matrix of second derivatives of the potential V ( R 1 , R 2 , … , R N ) {\displaystyle

Lorentzian manifold. Its metric tensor is in coordinates with the same symmetric matrix at every point of M, and its arguments can, per above, be taken as

usually done by one-parameter semigroups theory: for instance, if A is a symmetric matrix, then the elliptic operator defined by A u ( x ) := ∑ i , j ∂ x i a

transpose is replaced with the conjugate transpose. For a real-valued symmetric matrix, the Magnus-Neudecker derivative is established. Since for invertible

and C. One option is to turn an asymmetric matrix of size N into a symmetric matrix of size 2N. To double the size, each of the nodes in the graph is duplicated

q_{i}}}\cdot {\frac {\partial \mathbf {r} }{\partial q_{j}}}} is a symmetric matrix that is defined for the derivation. At every time instant t, the energy

{\displaystyle P,Q} and R {\displaystyle R} are the invariants of the symmetric matrix Γ j k {\displaystyle \Gamma _{jk}} . The matrix Γ j k {\displaystyle

y_{i}\\x_{j}&y_{j}\end{vmatrix}}=x_{i}y_{j}-x_{j}y_{i}.} (the skew symmetric matrix whose elements are pij is also called the Plücker matrix ) This implies

_{i}c_{i}(t)\mathbf {v} _{i}.} Plugging into the original expression (because L is a symmetric matrix, its unit-norm eigenvectors v i {\textstyle \mathbf {v} _{i}} are orthogonal):

closed; see normal scheme. null-polarity A correlation given by a skew symmetric matrix. A null-polarity of the projective space of a vector space is essentially

{\displaystyle \theta ^{bc}(x)} is an arbitrary position-dependent skew symmetric matrix, we see that local Lorentz and rotation invariance both requires and

of quantities F m m ′ {\displaystyle F_{mm'}} itself forms a real symmetric matrix, that depends only on the Euler angle β {\displaystyle \beta } , as

from the spectral theorem of linear algebra that a positive-definite symmetric matrix S has a unique positive-definite symmetric square root S1/2. We can

matrices. Then we find the eigenvalues and eigenvectors of the real symmetric matrix U ρ = T ρ T T ρ {\displaystyle U_{\rho }=T_{\rho }^{\text{T}}T_{\rho

_{2}){\boldsymbol {\sigma }}_{k}^{i}} . A convenient basis consists of one anti-symmetric matrix (with total spin S = 0 {\displaystyle S=0} , corresponding to a singlet

A_{ij}^{(a)}={\tfrac {1}{2}}\left(A_{ij}-A_{ji}\right).} The contraction of any symmetric matrix B with an arbitrary matrix A is i.e., the anti-symmetric component

− I k l . {\displaystyle \{\xi ^{k},\xi ^{l}\}=-I^{kl}.} The skew-symmetric matrix I k l {\displaystyle I^{kl}} , ‖ I ‖ = ‖ 0 − E n E n 0 ‖ , {\displaystyle

such a broad domain of applications. Since Σ is a positive definite symmetric matrix, it possesses a set of orthonormal eigenvectors forming a basis of

coordinates may be obtained by application of Wilson's GF method. The 3 × 3 symmetric matrix μ {\displaystyle {\boldsymbol {\mu }}} is called the effective reciprocal

\end{cases}}} Let M {\textstyle M} be a real n × n {\textstyle n\times n} symmetric matrix, then the Kibble–Slepian formula states that det ( I + M ) − 1 2 e

{k}}}\left({\bf {r}}\right)} . It is more convenient to deal with a symmetric matrix for the coefficients, and this can be done by defining c l m i = ∑

A T ≥ 0 {\displaystyle A=A^{T}\geq 0} is a positive semi-definite symmetric matrix, the logarithmic barrier f ( x ) = − log ⁡ ϕ ( x ) {\displaystyle f(x)=-\log

SL(2,C). Autonne–Takagi factorization states that for any complex symmetric matrix M, there is a unitary matrix U such that UMUt is diagonal. IfS is a

543–548). Archaic. Pfaffian A square root of the determinant of a skew-symmetric matrix. pippian An old name for the Cayleyan. plagiogonal Related to or fixed

z)=C\cdot \exp \,{1 \over 2}(pz^{2}+2qwz+rw^{2})} for which the complex symmetric matrix ( p q q r ) {\displaystyle {\begin{pmatrix}p&q\\q&r\end{pmatrix}}}