Diagonalizing a Matrix: Steps and Verification

[Deimantas]

Homework Statement

Diagonalize matrix

using only row/column switching; multiplying row/column by a scalar; adding a row/column, multiplied by some polynomial, to another row/column.

Homework Equations

The Attempt at a Solution

After diagonalization I get a diagonal matrix that looks like this

. What's the easiest way to tell if the answer is correct/incorrect?

 

[andrewkirk]

One way to tell is to build up the matrices A and B that represent the transformations that you preform in the diagonalisation process. If you've done that then you just need to perform the matrix multiplication ADB where D is the diagonal matrix, and check that it's equal to the original matrix M.

If the diagonal matrix is of eigenvalues (I can't recall whether they will be for general diagonalisation), another way might be to check that the characteristic equation of M is $(\lambda-1)^2(\lambda-(x^5+x^4-1))$.

 

[Deimantas]

One way to tell is to build up the matrices A and B that represent the transformations that you preform in the diagonalisation process. If you've done that then you just need to perform the matrix multiplication ADB where D is the diagonal matrix, and check that it's equal to the original matrix M.

If the diagonal matrix is of eigenvalues (I can't recall whether they will be for general diagonalisation), another way might be to check that the characteristic equation of M is $(\lambda-1)^2(\lambda-(x^5+x^4-1))$.

Wolfram suggests these eigenvalues

. I must have made some mistakes then.

 

[Ray Vickson]

Homework Statement

Diagonalize matrixView attachment 92744 using only row/column switching; multiplying row/column by a scalar; adding a row/column, multiplied by some polynomial, to another row/column.

Homework Equations

The Attempt at a Solution

After diagonalization I get a diagonal matrix that looks like this View attachment 92745 . What's the easiest way to tell if the answer is correct/incorrect?

Show us the actual steps you took; that way we can check if you have made any errors.