Question

(1) A square matrix with entries aj,k , j, k = 1, ..., n, is called...

  1. (1) A square matrix with entries aj,k , j, k = 1, ..., n, is called diagonal if aj,k = 0 whenever j is not equal to k. Show that the product of two diagonal n × n-matrices is again diagonal.

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
The trace of a square n×nn×n matrix A=(aij)A=(aij) is the sum a11+a22+⋯+anna11+a22+⋯+ann of the entries on...
The trace of a square n×nn×n matrix A=(aij)A=(aij) is the sum a11+a22+⋯+anna11+a22+⋯+ann of the entries on its main diagonal. Let VV be the vector space of all 2×22×2 matrices with real entries. Let HH be the set of all 2×22×2 matrices with real entries that have trace 11. Is HH a subspace of the vector space VV? Does HH contain the zero vector of VV? choose H contains the zero vector of V H does not contain the zero vector...
Let M be an n x n matrix with each entry equal to either 0 or...
Let M be an n x n matrix with each entry equal to either 0 or 1. Let mij denote the entry in row i and column j. A diagonal entry is one of the form mii for some i. Swapping rows i and j of the matrix M denotes the following action: we swap the values mik and mjk for k = 1,2, ... , n. Swapping two columns is defined analogously. We say that M is rearrangeable if...
A stochastic matrix is a square matrix A with entries 0≤a_ij≤1 such that the sum of...
A stochastic matrix is a square matrix A with entries 0≤a_ij≤1 such that the sum of each column of A is 1. Prove that if A is stochastic, then A^k is stochastic for every positive integer k.
*** Write a function called reverse_diag that creates a square matrix whose elements are 0 except...
*** Write a function called reverse_diag that creates a square matrix whose elements are 0 except for 1s on the reverse diagonal from top right to bottom left. The reverse diagonal of an n-by-n matrix consists of the elements at the following indexes: (1, n), (2, n-1), (3, n-2), … (n, 1). The function takes one positive integer input argument named n, which is the size of the matrix, and returns the matrix itself as an output argument. Note that...
For an n×n matrix, A, the trace of A is defined as the sum of the...
For an n×n matrix, A, the trace of A is defined as the sum of the entries on the main diagonal. That is, tr(A)=a11+a22+?+ann. (a) Prove that for any matrices A and B having the same size, tr(A+B)=tr(A)+tr(B) and for any scalar c, tr(cA)=ctr(A) (b) Prove tr(A)=tr(AT) for all square matrices A. (c) Prove that for any matrices A and B having the same size, tr(AB)=tr(BA). (d) Using (c), prove that if A and B are similar tr(A)=tr(B).
Show that if a square matrix K over Zp ( p prime) is involutory ( or...
Show that if a square matrix K over Zp ( p prime) is involutory ( or self-inverse), then det K=+-1 (An nxn matrix K is called involutory if K is invertible and K-1 = K) from Applied algebra show details
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.
For the general case of n masses coupled by n +1 springs, the mass matrix M...
For the general case of n masses coupled by n +1 springs, the mass matrix M 1) is a (n+1) x (n+1) diagonal matrix (i.e. all off-diagonal elements are identically equal to zero). 2) is a (n+1) x (n+1) non-diagonal matrix (i.e it has non-zero off-diagonal elements). 3) is a (n) x (n) diagonal matrix (i.e. all off-diagonal elements are identically equal to zero). 4) is a (n) x (n) non-diagonal matrix (i.e it has non-zero off-diagonal elements).
Let A be an n×n matrix. If there exists k > n such that A^k =0,then...
Let A be an n×n matrix. If there exists k > n such that A^k =0,then (a) prove that In − A is nonsingular, where In is the n × n identity matrix; (b) show that there exists r ≤ n such that A^r= 0.
n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M....
n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M. 1. Show that the diagonal of an anti-symmetric matrix are zero 2. suppose that A,B are symmetric n × n-matrices. Prove that AB is symmetric if AB = BA. 3. Let A be any n×n-matrix. Prove that A+A^t is symmetric and A - A^t antisymmetric. 4. Prove that every n × n-matrix can be written as the sum of a symmetric and anti-symmetric matrix.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT