Suppose the topic is the real space dimension of realistic square matrix multiplied by the usual addition number, and other situations are similar. As shown in the figure:

The elements in the symmetric matrix are symmetric about the main diagonal, so as long as the elements in the upper triangle or the lower triangle in the matrix are stored, every two symmetry element can enjoy a storage space. This can save nearly half of the storage space.

introduce

In linear algebra, a symmetric matrix is a square matrix, and its transposed matrix is equal to itself. In 1855, emmett (C. Hermite, 1822- 190 1) proved the special properties of the characteristic roots of some matrix classes discovered by other mathematicians, such as the characteristic roots of emmett matrix.

Later, Klebsch (A A. Clebsch, 183 1- 1872) and A.Buchheim proved the characteristic root property of symmetric matrices. H.Taber introduced the concept of trace of matrix and gave some related conclusions.