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An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

A positive definite function f on a group G is a function for which the matrix {f(x_ix_j^(-1))} is always positive semidefinite Hermitian.

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 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 ...

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

A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

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 ...

A mathematical object is said to be symmetric if it is invariant ("looks the same") under a symmetry transformation. A function, matrix, etc., is symmetric if it remains ...

The numbers of positive definite n×n matrices of given types are summarized in the following table. For example, the three positive eigenvalues 2×2 (0,1)-matrices are [1 0; 0 ...

A square matrix is said to be totally positive if the determinant of any square submatrix, including the minors, is positive. For instance, any 2×2 matrix whose determinant ...