Square root of a matrix information

the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product...

A square root of a 2×2 matrix M is another 2×2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself. In general, there can...

mathematics, a square root of a number x is a number y such that y 2 = x {\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of multiplying...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

matrix sign function is a matrix function on square matrices analogous to the complex sign function. It was introduced by J.D. Roberts in 1971 as a tool...

mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization...

Householder matrix is built through the identity matrix) Square root of a 2 by 2 identity matrix Unitary matrix Zero matrix "Identity matrix: intro to identity...

such as square root of a matrix, matrix exponential, and logarithm of a matrix are basic examples of hypercomplex analysis. The function theory of diagonalizable...

instance, a partial differential equation on a square domain (using central differences) will yield a matrix with a bandwidth equal to the square root of the...

every real number other than zero (which has one double square root). In contexts in which use of the letter i is ambiguous or problematic, the letter j...

square matrix A is called invertible (also nonsingular, nondegenerate or —rarely used— regular) if there exists an n-by-n square matrix B such that A...

A root of degree 2 is called a square root (usually written without the n as just x {\displaystyle {\sqrt {x}}} ) and a root of degree 3, a cube root...

{\displaystyle p(x)=c_{0}+c_{1}x+\cdots +c_{n-1}x^{n-1}+x^{n}} is the square matrix defined as C ( p ) = [ 0 0 … 0 − c 0 1 0 … 0 − c 1 0 1 … 0 − c 2 ⋮ ⋮...

Let A {\displaystyle \mathbf {A} } be a positive semi-definite Hermitian matrix. Then it can be written as a product of its square root matrix, A = B...

(see Inverse trigonometric functions#Logarithmic forms, Matrix logarithm, Square root of a matrix) sinh ⁡ X = e X − e − X 2 cosh ⁡ X = e X + e − X 2 {\displaystyle...

In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...

acceptable model fit. The root mean square residual (RMR) and standardized root mean square residual (SRMR) are the square root of the discrepancy between...

= B B {\displaystyle M=BB} . This matrix B {\displaystyle B} is unique, is called the non-negative square root of M {\displaystyle M} , and is denoted...

spectral theorem. A (nonzero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies a linear equation of the form A v = λ v {\displaystyle...

field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation...

of a matrix A {\displaystyle A} is the largest singular value of A {\displaystyle A} (i.e., the square root of the largest eigenvalue of the matrix A...

Umeyama, is a method for calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points....

When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output,...

a scalar value that is a certain function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|...

error of each coefficient β ^ j {\displaystyle \scriptstyle {\hat {\beta }}_{j}} is equal to square root of the j-th diagonal element of this matrix. The...

mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are...