Question

Is it true that if detA = detB, then there exist an invertable matrix P such...

Is it true that if detA = detB, then there exist an invertable matrix P such that AP = PB? Please give proof.

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
Give a proof base on the proof of the Determinant of a Vandermonde matrix that the...
Give a proof base on the proof of the Determinant of a Vandermonde matrix that the INTERPOLATING POLYNOMIAL exist and its unique.
Is it true that for a QM operator in its matrix form must be in the...
Is it true that for a QM operator in its matrix form must be in the same basis that the state its acting on for the matrix multiplication to make sense. For example for me to multiply the matrix form of the Hamiltonian of the system with an eigenfunction of the hamiltonian should all the matrix elements for the hamiltonian operator be made using the eigenbasis of the hamiltonian. If so then please provide a proof. If this isnt the...
If a , b ∈ N , then there exist unique integers q and r for...
If a , b ∈ N , then there exist unique integers q and r for which a = b q + r and 0 ≤ r < q .Is this statement true? If yes, give a proof of the statement. If not, give a counterexample.
Let A be an n x n invertable and diagonalizable matrix. Is A^2 diagonalizable? Please give...
Let A be an n x n invertable and diagonalizable matrix. Is A^2 diagonalizable? Please give proof.
We say the a matrix A is similar to a matrix B if there is some...
We say the a matrix A is similar to a matrix B if there is some invertible matrix P so that B=P^-1 AP. Show that if A and B are similar matrices and b is an eigenvalue for B, then b is also an eigenvalue for A. How would an eigenvector for B associated with b compare to an eigenvector for A?
Let P be a 2 x 2 stochastic matrix. Prove that there exists a 2 x...
Let P be a 2 x 2 stochastic matrix. Prove that there exists a 2 x 1 state matrix X with nonnegative entries such that P X = X. Hint: First prove that there exists X. I then proved that x1 and x2 had to be the same sign to finish off the proof
Let A be an n × n-matrix. Show that there exist B, C such that B...
Let A be an n × n-matrix. Show that there exist B, C such that B is symmetric, C is skew-symmetric, and A = B + C. (Recall: C is called skew-symmetric if C + C^T = 0.) Remark: Someone answered this question but I don't know if it's right so please don't copy his solution
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.
A projection matrix (or a projector) is a matrix P for which P2 = P. a)...
A projection matrix (or a projector) is a matrix P for which P2 = P. a) (10 pts) Find the eigenvalues of a projector. Show details. b) (10 pts) Show that if P is a projector, then (I – P) is also projector. Explain briefly. c) (5 pts) What assumption about matrix A should be made to run the power method?
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...