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The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

The power A^n of a matrix A for n a nonnegative integer is defined as the matrix product of n copies of A, A^n=A...A_()_(n). A matrix to the zeroth power is defined to be the ...

An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...

A diagonal matrix is a square matrix A of the form a_(ij)=c_idelta_(ij), (1) where delta_(ij) is the Kronecker delta, c_i are constants, and i,j=1, 2, ..., n, with no implied ...

A zero matrix is an m×n matrix consisting of all 0s (MacDuffee 1943, p. 27), denoted 0. Zero matrices are sometimes also known as null matrices (Akivis and Goldberg 1972, p. ...

A matrix for which horizontal and vertical dimensions are not the same (i.e., an m×n matrix with m!=n).

A square matrix A such that A^2=I, where I is the identity matrix. An involutory matrix is its own matrix inverse.

A square matrix A is antihermitian if it satisfies A^(H)=-A, (1) where A^(H) is the adjoint. For example, the matrix [i 1+i 2i; -1+i 5i 3; 2i -3 0] (2) is an antihermitian ...

A positive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a positive number, i.e., a_(ij)>0 for all i, j. Positive matrices are therefore a ...