In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. Some particular...

analysis. Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. The determinant of a square matrix is...

Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple...

\omega _{3}} does not vary much, and write the equations of motion as a matrix equation: d d t [ ω 1 ω 2 ] = [ 0 − ω 3 ( I 3 − I 2 ) / I 1 − ω 3 ( I 1...

data matrix. PCA is the simplest of the true eigenvector-based multivariate analyses and is closely related to factor analysis. Factor analysis typically...

growth–share matrix (also known as the product portfolio matrix, Boston Box, BCG-matrix, Boston matrix, Boston Consulting Group portfolio analysis and portfolio...

analysis. The spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix A...

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...

columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...

In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U...

In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict...

In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to...

In chemical analysis, matrix refers to the components of a sample other than the analyte of interest. The matrix can have a considerable effect on the...

algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors...

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A  is symmetric ⟺ A = A T . {\displaystyle A{\text{...

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field...

Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra...

In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

approaches (these include approaches like framework analysis, template analysis and matrix analysis) and reflexive approaches. They first described their...

in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper...

and strategic management, SWOT analysis (also known as the SWOT matrix, TOWS, WOTS, WOTS-UP, and situational analysis) is a decision-making technique...

In linear algebra, the Gram matrix (or Gramian matrix, Gramian) of a set of vectors v 1 , … , v n {\displaystyle v_{1},\dots ,v_{n}} in an inner product...

complex matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though that...

In mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose...

Charles R. (1985), Matrix Analysis, Cambridge University Press, ISBN 978-0-521-38632-6. Meyer, Carl D. (2000), Matrix Analysis and Applied Linear Algebra...

specifically the problem of statistical classification, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the...

particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For example, when solving...