# Matrix Classification

The section describes a set of functions for analyzing the structural properties of matrices. These methods allow us to determine whether a matrix is symmetric, Hermitian, diagonal, triangular, trapezoidal, Hessenberg, bidiagonal, or scalar. Such a classification simplifies the selection of efficient algorithms for linear algebra and optimization of computations.

| Function | Action |
| --- | --- |
| IsSymmetric | Check if a square matrix is symmetric |
| IsHermitian | Check if a square complex matrix is Hermitian |
| IsUpperTriangular | Check if a square matrix is upper triangular |
| IsLowerTriangular | Check if a square matrix is lower triangular |
| IsTrapezoidal | Check if a rectangular (not square) m-by-n matrix is upper or lower trapezoidal |
| IsUpperHessenberg | Check if a square matrix is upper Hessenberg matrix |
| IsLowerHessenberg | Check if a square matrix is lower Hessenberg matrix |
| IsTridiagonal | Check if a square matrix is tridiagonal |
| IsUpperBidiagonal | Check if a square matrix is upper bidiagonal |
| IsLowerBidiagonal | Check if a square matrix is lower bidiagonal |
| IsDiagonal | Check if a square matrix is diagonal |
| IsScalar | Check if a square matrix is scalar matrix |