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A square matrix which is not reducible is said to be irreducible.

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

A nonpositive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a nonpositive number, i.e., a_(ij)<=0 for all i, j. Nonpositive matrices are ...

Matrix decomposition refers to the transformation of a given matrix (often assumed to be a square matrix) into a given canonical form.

An n×n matrix A is an elementary matrix if it differs from the n×n identity I_n by a single elementary row or column operation.

A unit matrix is an integer matrix consisting of all 1s. The m×n unit matrix is often denoted J_(mn), or J_n if m=n. Square unit matrices J_n have determinant 0 for n>=2. An ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

A periodic matrix with period 1, so that A^2=A.

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only ...

The rank of a matrix or a linear transformation is the dimension of the image of the matrix or the linear transformation, corresponding to the number of linearly independent ...