2.3 Symmetric Matrices

A symmetric matrix is a square matrix that satisfies where denotes the transpose of . That is, for all . For example, this is a 4 x 4 symmetric matrix:

Symmetric matrices are often used to represent quadratic forms.

NMath Matrix provides symmetric matrix classes for single- and double-precision floating point numbers. The classnames are FloatSymmetricMatrix and DoubleSymmetricMatrix. Hermitian matrices are a generalization of symmetric matrices for complex types (Section 2.4).

For efficiency, only the upper triangle is stored. The storage scheme is the same as for an upper triangular matrix (Section 2.2).