Some special matrices and algebraic properties

In linear algebra, square matrices, diagonal matrices, identity matrices, triangular matrices, and symmetric matrices are fundamental matrices. Apart from these matrices, there are also some special matrices.In this thesis, special matrices with particularly important applicatios are introduced, including alternate matrices such as Vandermonde and Moore matrices, anti-diagonal matrices, band matrices, Toeplitz matrices, Boolean matrices, bi-symmetric matrices, Cauchy matrices, Hankel matrices, Frobenius matrices, Hessenberg matrices, Walsh matrices, Hadamard matrices, and Hollow matrices. The application areas of these matrices and the algebraic properties of the sets formed by these matrices are given.