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
Famous quotes containing the words special and/or properties:
“It is a maxim among these lawyers, that whatever hath been done before, may legally be done again: and therefore they take special care to record all the decisions formerly made against common justice and the general reason of mankind.”
—Jonathan Swift (1667–1745)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)