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.)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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.]
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.
Prove that if an m x m matrix A is upper-triangular, then A-1 is also upper-triangular....
Prove that if an m x m matrix A is upper-triangular, then A-1 is also upper-triangular. Hint: Obtain Axj=ej where xj is the jth column of A-1 and ej is the jth column of I. Then use back substitution to argue that xij = 0 for i > j.
For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal....
For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not possible, enter IMPOSSIBLE.) A = 6 −3 −2 1 . Verify that P−1AP is a diagonal matrix with the eigenvalues on the main diagonal.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT