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:
“When we walk the streets at night in safety, it does not strike us that this might be otherwise. This habit of feeling safe has become second nature, and we do not reflect on just how this is due solely to the working of special institutions. Commonplace thinking often has the impression that force holds the state together, but in fact its only bond is the fundamental sense of order which everybody possesses.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“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)