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If two square n×n matrices A and B are simultaneously upper triangularizable by similarity transforms, then there is an ordering a_1, ..., a_n of the eigenvalues of A and ...

A matrix with 0 determinant whose determinant becomes nonzero when any element on or below the diagonal is changed from 0 to 1. An example is M=[1 -1 0 0; 0 0 -1 0; 1 1 1 -1; ...

A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...

The kernel of a module homomorphism f:M-->N is the set of all elements of M which are mapped to zero. It is the kernel of f as a homomorphism of additive groups, and is a ...

A nonempty finite set of n×n integer matrices for which there exists some product of the matrices in the set which is equal to the zero matrix.

For a given n, is the problem of determining if a set is mortal solvable? n=1 is solvable, n=2 is unknown, and n>=3 is unsolvable.

A negative definite matrix is a Hermitian matrix all of whose eigenvalues are negative. A matrix m may be tested to determine if it is negative definite in the Wolfram ...

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 negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive. A matrix m may be tested to determine if it is negative semidefinite in the ...

There are two equivalent definitions for a nilpotent matrix. 1. A square matrix whose eigenvalues are all 0. 2. A square matrix A such that A^n is the zero matrix 0 for some ...