On factorization and calculation of determinant of block matrices whose submatrices are triangular

In this thesis, we consider a block matrix A whose components are n×n triangular matrices. This thesis aims to prove that the determinant of the matrix A is solely determined by the diagonal elements of its submatrices and this determinant is expressed as the multiplication of some subdeterminants. This work also aims to study on the adjoint matrix, eigenvalues, the inverse and factorization of the matrix A.