Monday
April 21, 2014

Homework Help: linear algebra

Posted by mathstudent on Friday, July 20, 2007 at 2:19pm.

if:
A and B are matrices
and A^2 is similar to B^2

Is A guaranteed to be similar to B?


-------
Matrix similarity means that the matrices are identical if one of the matrices is converted to another basis. If matrices C and D are similar:

C = P^-1 * D * P

where P converts from standard basis to alternate basis B, and P^-1 is the inverse.

Counterexample: take A to be the identity matrix and define B by changing a 1 to -1 somewhere on the diagonal. Then A^2 = B^2, but A is not equal to B.

No transformation of the form
P A P^(-1) can make A equal to B. If two matrices are similar and diagonizable, then both matrices can be obtained from the same diagonal matrix using different transformaton matrices.

So, in diagonalized form they must be the same. But B and A are already in diagonalized form and are not the same.

great counterexample. thanks count.

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

matrices - Two matrices can be multiplied only if their sizes are compatible. ...
Math - I have a few questions about T-Matrix. In excel, I am suppose to work ...
Algebra II (Matrices) - My book doesn't solve it like a linear equation, they ...
linear algebra - Prove that the trace is a similarity invariant. In other words...
math - Two matrices can be multiplied only if their sizes are compatible. ...
Math (matrices) - No one answered my matrix question. Let me rephrase: Let A, B...
Algebra II - Can a matrix have a two digit number? I have to add the matrices[3 ...
Linear algebra - find the inverse of the following matrices if they exist. [1 -2...
Algebra-Matrix - How would I do these Matrices? 1. |1/2 14 10 -8| 2, Let matrix ...
Maths: Algebra Matrices Class 12th - matrix{{0, 1, -1}, {2, 1, 3}, {1, 1, 1}} ...

Search
Members