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:
“Personal prudence, even when dictated by quite other than selfish considerations, surely is no special virtue in a military man; while an excessive love of glory, impassioning a less burning impulse, the honest sense of duty, is the first.”
—Herman Melville (18191891)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (16321704)