Theorem
- (a) The transpose of a lower triangular matrix is upper triangular, and the transpose of an upper triangular matrix is lower triangular.
- (b) The product of lower triangular matrices is lower triangular, and the product of upper triangular matrices is upper triangular.
Inverse
- (c) A triangular matrix is invertible if and only if its diagonal entries are all nonzero.
- (d) The inverse of an invertible lower triangular matrix is lower triangular, and the inverse of an invertible upper triangular matrix is upper triangular.