- #1

- 125

- 0

Thanks

Tal

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter talolard
- Start date

- #1

- 125

- 0

Thanks

Tal

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 966

[tex]\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}[/tex]

and

[tex]\begin{bmatrix}\frac{1}{2} & 0 \\ 0 & 2\end{bmatrix}[/tex]

have the same determinant but are not similar.

Also both

[tex]\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}[/tex]

and

[tex]\begin{bmatrix}2 & 0 \\ 0 & 0\end{bmatrix}[/tex]

have the same trace but are not similar.

And, just in case you were wondering,

[tex]\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}[/tex]

and

[tex]\begin{bmatrix}1 & 1 \\ 0 & 1\end{bmatrix}[/tex]

have the same determinant

In order to be similar, two matrices must have the same eigenvalues and the same number of independent eigenvectors corresponding to each eigenvalue.

- #3

- 125

- 0

Great, Thanks.

Share:

- Replies
- 7

- Views
- 3K