complex square matrix A is normal if it commutes with its conjugate transpose A*: A  normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{ normal}}\iff A^{*}A=AA^{*}...

.} The matrix X T X {\displaystyle \mathbf {X} ^{\operatorname {T} }\mathbf {X} } is known as the normal matrix or Gram matrix and the matrix X T y {\displaystyle...

X_{k})^{\mathrm {T} }} is called a centered normal random vector if there exists a k × ℓ {\displaystyle k\times \ell } matrix A {\displaystyle {\boldsymbol {A}}}...

the matrix normal distribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariate normal distribution...

mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n {\displaystyle...

matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition"...

given by a square matrix M, then its Jordan normal form is also called the Jordan normal form of M. Any square matrix has a Jordan normal form if the field...

In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries...

Any normal matrix is similar to a diagonal matrix, since its Jordan normal form is diagonal. Eigenvectors of distinct eigenvalues of a normal matrix are...

y⟩. U is normal ( U ∗ U = U U ∗ {\displaystyle U^{*}U=UU^{*}} ). U is diagonalizable; that is, U is unitarily similar to a diagonal matrix, as a consequence...

approximating numerically selected eigenvectors of the normal matrix A = M ∗ M {\displaystyle A=M^{*}M} . The matrix M = [ 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

real symmetric matrix and more generally a Hermitian matrix, and a unitary matrix, is never defective; more generally, a normal matrix (which includes...

(conjugate transpose) of Q, and therefore normal (Q∗Q = QQ∗) over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation...

entries of a matrix. Anti-diagonal matrix Banded matrix Bidiagonal matrix Diagonally dominant matrix Diagonalizable matrix Jordan normal form Multiplication...

linear algebra, a square matrix A {\displaystyle A}  is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists...

Normal map may refer to: Normal mapping in 3D computer graphics Normal invariants in mathematical surgery theory Normal matrix in linear algebra Normal...

{H}}\right)} Bivector (complex) Hermitian matrix Normal matrix Skew-symmetric matrix Unitary matrix Horn & Johnson (1985), §4.1.1; Meyer (2000), §3...

matrix A {\displaystyle A} . A (real-valued) symmetric matrix is necessarily a normal matrix. Denote by ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot...

self-adjoint). A normal matrix is the matrix expression of a normal operator on the Hilbert space C n {\displaystyle \mathbb {C} ^{n}} . Normal operators are...

Gram matrix G {\displaystyle G} is also a normal matrix. The Gram matrix of any orthonormal basis is the identity matrix. Equivalently, the Gram matrix of...

player) and yields a representation of payoff as its output. The matrix provided is a normal-form representation of a game in which players move simultaneously...

the special case where ⁠ A {\displaystyle A} ⁠ is a normal matrix (for example, a Hermitian matrix), the pseudoinverse ⁠ A + {\displaystyle A^{+}} ⁠ annihilates...

In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices...

The singular values are the absolute values of the eigenvalues of a normal matrix A, because the spectral theorem can be applied to obtain unitary diagonalization...

matrix A, one is interested in finding a simple "normal form" B which is similar to A—the study of A then reduces to the study of the simpler matrix B...

transformation when transforming surface normals. The inverse transpose is equal to the original matrix if the matrix is orthonormal, that is, purely rotational...

slow motion while the camera appears to move through the scene at normal speed. The Matrix opened in theaters in the United States on March 31, 1999, to widespread...

In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column...