Question

Show that if A is an (n × n) upper triangular matrix or lower triangular matrix,...

Show that if A is an (n × n) upper triangular matrix or lower triangular matrix, its eigenvalues are the entries on its main diagonal. (You may limit yourself to the (3 × 3) case.)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
THEOREM (a) The transpose of a lower triangular matrix is upper triangular, and the transpose of...
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. (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...
1. Determine if the statements are true or false: a. The eigenvalues of a lower triangular...
1. Determine if the statements are true or false: a. The eigenvalues of a lower triangular matrix are the diagonal entries of the matrix. b. For every square matrix A, the sum of all the eigenvalues of A is equal to the sum of all the diagonal entries of A.
Prove: Why must every upper triangular matrix with no zero entries on the main diagonal be...
Prove: Why must every upper triangular matrix with no zero entries on the main diagonal be nonsingular? (Linear Algebra)
A triangular matrix is called unit triangular if it is square and every main diagonal element...
A triangular matrix is called unit triangular if it is square and every main diagonal element is a 1. (a) If A can be carried by the gaussian algorithm to row-echelon form using no row interchanges, show that A = LU where L is unit lower triangular and U is upper triangular. (b) Show that the factorization in (a) is unique.
Show that the product of arbitrarily many upper (or lower)-triangular matrices is upper (or lower)-triangular.
Show that the product of arbitrarily many upper (or lower)-triangular matrices is upper (or lower)-triangular.
Show that for each nonsingular n x n matrix A there exists a permutation matrix P...
Show that for each nonsingular n x n matrix A there exists a permutation matrix P such that P A has an LR decomposition. [note: A factorization of a matrix A into a product A=LR of a lower (left) triangular matrix L and an upper (right) triangular matrix R is called an LR decomposition of A.]
Show that a triangular matrix is normal if and only if it is diagonal. Please use...
Show that a triangular matrix is normal if and only if it is diagonal. Please use clear, intelligable writing.
Consider the proposed matrix factorization: A = LS, where L is lower triangular with 1’s on...
Consider the proposed matrix factorization: A = LS, where L is lower triangular with 1’s on the diagonal, and S is symmetric. (a) Show how the LU decomposition can be used to derive this factorization. (b) What conditions must A satisfy for this factorization to exist?
If TL (n ,F) and STL(n,F) denote the (upper) triangular and special (upper) triangular groups of...
If TL (n ,F) and STL(n,F) denote the (upper) triangular and special (upper) triangular groups of degree n over G respectively , show that the commutator subgroup of TL(n ,F) is a subgroup of STL (n , F) while STL (n,F) is nilpotent of class n-1.
3.35 Show that if A is an m x m symmetric matrix with its eigenvalues equal...
3.35 Show that if A is an m x m symmetric matrix with its eigenvalues equal to its diagonal elements, then A must be a diagonal matrix.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT