Saturday

April 18, 2015

April 18, 2015

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

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**

**Related Questions**

matrices - Two matrices can be multiplied only if their sizes are compatible. ...

linear algebra - Prove that the trace is a similarity invariant. In other words...

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 ...

Math (matrices) - No one answered my matrix question. Let me rephrase: Let A, B...

math - Two matrices can be multiplied only if their sizes are compatible. ...

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...

Math: matrices - If A and B are both square n x n matrices, If AB = I, prove BA...

Precalculus - Find the values of x and y. Matrices.. [-4 2 3 5 3 5 2 -3 1] TIMES...