In linear algebra, the identity matrix of size n {\displaystyle n} is the n × n {\displaystyle n\times n} square matrix with ones on the main diagonal...
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algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing...
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denoted by A−1. Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity matrix. Over a field...
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In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices...
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Determinant (redirect from Matrix determinant)
square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the...
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square matrix of order n, and also a special kind of diagonal matrix. It is called an identity matrix because multiplication with it leaves a matrix unchanged:...
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rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...
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is the identity matrix. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is...
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matrix A {\displaystyle A} of dimension n × n {\displaystyle n\times n} may be found by appending the n × n {\displaystyle n\times n} identity matrix...
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QT is the transpose of Q and I is the identity matrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal...
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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...
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{I} ,} where I is the identity matrix of the same size as A. Consequently, the multiplicative inverse of an invertible matrix can be found by dividing...
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{X}{k}}\right)^{k}} where I is the n×n identity matrix. When X is an n×n diagonal matrix then exp(X) will be an n×n diagonal matrix with each diagonal element equal...
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{smallmatrix}}\right]} . An identity matrix of any size, or any multiple of it is a diagonal matrix called a scalar matrix, for example, [ 0.5 0 0 0.5...
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idempotent. The only non-singular idempotent matrix is the identity matrix; that is, if a non-identity matrix is idempotent, its number of independent rows...
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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...
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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...
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real rotation matrix is the identity matrix. Likewise, the Gram matrix of the rows or columns of a unitary matrix is the identity matrix. The rank of the...
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In a topological space, the identity function is always continuous. The identity function is idempotent. Identity matrix Inclusion map Indicator function...
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n} identity matrix. Involutory matrices are all square roots of the identity matrix. This is a consequence of the fact that any invertible matrix multiplied...
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Pauli matrices (redirect from Pauli matrix)
(right/left). Each Pauli matrix is Hermitian, and together with the identity matrix I (sometimes considered as the zeroth Pauli matrix σ0 ), the Pauli matrices...
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{\displaystyle I_{n}} is the n × n {\displaystyle n\times n} identity matrix. The matrix Ω {\displaystyle \Omega } has determinant + 1 {\displaystyle...
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is the identity matrix. If A {\textstyle A} is a skew-symmetric matrix then A 2 {\textstyle A^{2}} is a symmetric negative semi-definite matrix. As a result...
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rotation matrix. An infinitesimal rotation matrix has the form I + d θ A , {\displaystyle I+d\theta \,A,} where I {\displaystyle I} is the identity matrix, d...
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where A(L(G)) is the adjacency matrix of the line graph of G, B(G) is the incidence matrix, and Im is the identity matrix of dimension m. The discrete Laplacian...
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matrix there is a matrix A−1 that represents a transformation that "undoes" A since its composition with A is the identity matrix. In some practical...
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linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of...
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In mathematics, a symmetric matrix M {\displaystyle \ M\ } with real entries is positive-definite if the real number x ⊤ M x {\displaystyle \ \mathbf...
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Characteristic polynomial (redirect from Characteristic equation (matrix))
algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It...
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List of named matrices (redirect from List of matrix)
entries, including constant matrices. Important examples include the identity matrix given by I n = [ 1 0 ⋯ 0 0 1 ⋯ 0 ⋮ ⋮ ⋱ ⋮ 0 0 ⋯ 1 ] . {\displaystyle...
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