es of the matrix.[23] They may be complex even if the entries of A are real. According to the Cayley–Hamilton theorem, pA(A) = 0, that is to say, the characteristic polynomial applied to the matrix itself yields the zero matrix.සමමිතිය[සංස්කරණය]A square matrix A that is equal to its transpose, i.e., A = AT, is a symmetric matrix.  If instead, A was equal to the negative of its transpose, i.e., A = −AT, then A is a skew-symmetric matrix. In complex matrices, symmetry is often replaced by the concept of Hermitian matrices, which satisfy A∗ = A, where the star or asterisk denotes the conjugate transpose of the matrix, i.e., the transpose of the complex conjugate of A.By the spectral theorem, real symmetric matrices and complex Hermitian matrices have an eigenbasis; i.e., every vector is expressible as a linear combination of eigenvectors. In both cases, all eigenvalues are real.[24] This theorem can be generalized to infinite-dimensional situations related to matrices with infinite