Question

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.

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...
Suppose A and B are matrices in lower triangular form, show that A ˙ ×B [...
Suppose A and B are matrices in lower triangular form, show that A ˙ ×B [ Kronecker product of A and B] is also in lower triangular form. Furthermore, every eigenvalue of A ˙ ×B [Kronecker product of A and B] has the form of αβ, where α is an eigenvalue of A and β is an eigenvalue of B.
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.)
Suppose that A, B are upper triangular matrices in R 4×4 , that is, all entries...
Suppose that A, B are upper triangular matrices in R 4×4 , that is, all entries below the diagonal are equal to 0. Show that AB is also upper triangular. This fact holds in any R n×n , but we here specify 3 for simplicity
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.
A variable follows the triangular distribution and has a lower limit of 200, an upper limit...
A variable follows the triangular distribution and has a lower limit of 200, an upper limit of 1600, and the most likely value of 750. Find the following: a)Value of Standard Deviation b)Probability the variable is less than 600? c)Probability that variable is greater than 1000? d)Probability the variable is between 800 and 1000?
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.
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.
Show that the product of two n × n unitary matrices is unitary. Is the same...
Show that the product of two n × n unitary matrices is unitary. Is the same true of the sum of two n × n unitary matrices? Prove or find a counterexample.
Show/Prove that every invertible square (2x2) matrix is a product of at most four elementary matrices
Show/Prove that every invertible square (2x2) matrix is a product of at most four elementary matrices