Special Properties
A matrix which is simultaneously triangular and normal is also diagonal. This can be seen by looking at the diagonal entries of A*A and AA*, where A is a normal, triangular matrix.
The transpose of an upper triangular matrix is a lower triangular matrix and vice versa.
The determinant of a triangular matrix equals the product of the diagonal entries. Since for any triangular matrix A the matrix, whose determinant is the characteristic polynomial of A, is also triangular, the diagonal entries of A in fact give the multiset of eigenvalues of A (an eigenvalue with multiplicity m occurs exactly m times as diagonal entry).
Read more about this topic: Triangular Matrix
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