This document defines and explains different types of matrices: - Upper and lower triangular matrices have zeros above or below the main diagonal of a square matrix. - The determinant of a matrix is a scalar value obtained from the products of the matrix's elements according to certain constraints. - A banded matrix is a sparse matrix with nonzero elements confined to a diagonal band around the main diagonal. - The transpose of a matrix exchanges the rows and columns of the original matrix. - For matrix multiplication to be defined, the number of columns of the left matrix must equal the number of rows of the right matrix.