Square root of a 2 by 2 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...

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...

mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function...

M=BB} . This matrix B {\displaystyle B} is unique, is called the non-negative square root of M {\displaystyle M} , and is denoted with B = M 1 2 {\displaystyle...

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...

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...

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...

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...

a matrix function that maps square matrices with complex entries to square matrices of the same size. This is used for defining the exponential of a matrix...

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...

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

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 ⋮ ⋮ ⋱ ⋮ ⋮ 0 0 … 1 − c n − 1 ] . {\displaystyle...

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

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|...

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...

square root in the quadratic formula. If a ≠ 0 , {\displaystyle a\neq 0,} this discriminant is zero if and only if the polynomial has a double root....

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...

a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power n. Roots of unity...

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

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,...

}}_{j}} is equal to square root of the j-th diagonal element of this matrix. The estimate of this standard error is obtained by replacing the unknown...

matrix is Q = [ 1 − 2 y 2 − 2 z 2 2 x y − 2 z w 2 x z + 2 y w 2 x y + 2 z w 1 − 2 x 2 − 2 z 2 2 y z − 2 x w 2 x z − 2 y w 2 y z + 2 x w 1 − 2 x 2 − 2...

factorial ( 1 ! = 1 {\displaystyle 1!=1} ), its own square ( 1 2 = 1 {\displaystyle 1^{2}=1} ) and square root ( 1 = 1 {\displaystyle {\sqrt {1}}=1} ), its own...

norm of residuals is used for indicating goodness of fit. This term is calculated as the square-root of the sum of squares of residuals: norm of residuals...