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...

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...

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...

In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices...

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...

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:...

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 = [...

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...

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...

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...

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...

{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...

{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...

{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...

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...

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 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...

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...

In a topological space, the identity function is always continuous. The identity function is idempotent. Identity matrix Inclusion map Indicator function...

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...

(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...

{\displaystyle I_{n}} is the n × n {\displaystyle n\times n} identity matrix. The matrix Ω {\displaystyle \Omega } has determinant + 1 {\displaystyle...

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...

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...

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...

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...

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...

In mathematics, a symmetric matrix   M   {\displaystyle \ M\ } with real entries is positive-definite if the real number   x ⊤ M x   {\displaystyle \ \mathbf...

algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It...

entries, including constant matrices. Important examples include the identity matrix given by I n = [ 1 0 ⋯ 0 0 1 ⋯ 0 ⋮ ⋮ ⋱ ⋮ 0 0 ⋯ 1 ] . {\displaystyle...