Definitions

1. Two matrices A and B of the same order whose corresponding entries are equivalent are considered equal. That is: a_ij=b_ij i=1,...,n ; j=1,2,...,m.
2. A square matrix is a matrix which has the same number of rows and columns.
3. The main diagonal of a matrix is formed by the elements of a matrix starting in the upper left corner and proceeding down and to the right (a_ii).
4. A matrix with all-zero entries below the top-left-to-lower-right diagonal is called upper triangular.
5. A matrix with all-zero entries over the top-left-to-lower-right diagonal is called lower triangular.
6. A matrix with non-zero entries only on the diagonal is called diagonal.
7. A diagonal matrix whose non-zero entries are all 1's is called an identity matrix.
   The 3 × 3 identity is denoted by I₃ (pronounced as "eye-three" or "eye-sub-three"); similarly, the 4 × 4 identity is I₄ and the 5 × 5 identity matrix is I₅.
8. The transpose of a Matrix A is a matrix which is formed by turning all the rows of the given matrix into columns and vice-versa. The transpose of matrix A is written A^T.