Square matrix with ones on the main diagonal and zeros elsewhere
Not to be confused with matrix of ones, unitary matrix, or matrix unit.
In linear algebra, the identity matrix of size is the square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to multiplying by the number 1.
In linear algebra, the identitymatrix of size n {\displaystyle n} is the n × n {\displaystyle n\times n} square matrix with ones on the main diagonal...
algebra), the Woodbury matrixidentity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing...
In mathematics, an elementary matrix is a matrix which differs from the identitymatrix by one single elementary row operation. The elementary matrices...
is the identitymatrix. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is...
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 = [...
denotes the n-by-n identitymatrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined...
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...
QT is the transpose of Q and I is the identitymatrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal...
identitymatrix. We then reduce the part of (A|I2{\displaystyle (A\vert \mathbf {I} _{2}} corresponding to A{\displaystyle A} to the identitymatrix using...
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 identitymatrix of the same size as A. Consequently, the multiplicative inverse of an invertible matrix can be found by dividing...
d{smallmatrix}}\right]} . An identitymatrix of any size, or any multiple of it is a diagonal matrix called scalar matrix, for example, [ 0.5 0 0 0.5 ]...
{X}{k}}\right)^{k}} where I is the n×n identitymatrix. When X is an n×n diagonal matrix then exp(X) will be an n×n diagonal matrix with each diagonal element equal...
real rotation matrix is the identitymatrix. Likewise, the Gram matrix of the rows or columns of a unitary matrix is the identitymatrix. The rank of the...
{\displaystyle I_{n}} is the n × n {\displaystyle n\times n} identitymatrix. The matrix Ω {\displaystyle \Omega } has determinant + 1 {\displaystyle...
idempotent. The only non-singular idempotent matrix is the identitymatrix; that is, if a non-identitymatrix is idempotent, its number of independent rows...
In a topological space, the identity function is always continuous. The identity function is idempotent. Identitymatrix Inclusion map Indicator function...
(right/left). Each Pauli matrix is Hermitian, and together with the identitymatrix I (sometimes considered as the zeroth Pauli matrix σ0 ), the Pauli matrices...
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...
algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It...
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...
up identity in Wiktionary, the free dictionary. Identity may refer to: Identity document Identity (philosophy) Identity (social science) Identity (mathematics)...
entries, including constant matrices. Important examples include the identitymatrix given by I n = [ 1 0 ⋯ 0 0 1 ⋯ 0 ⋮ ⋮ ⋱ ⋮ 0 0 ⋯ 1 ] . {\displaystyle...
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