- #1

- 15

- 2

## Homework Statement

Let A be a nxn matrix, and I the corresponding identity matrix, both in the real numbers ℝ. Assume that A^m=0 for a positive integer m. Show that I-A is an invertible matrix.

- Thread starter Fosheimdet
- Start date

- #1

- 15

- 2

Let A be a nxn matrix, and I the corresponding identity matrix, both in the real numbers ℝ. Assume that A^m=0 for a positive integer m. Show that I-A is an invertible matrix.

- #2

lurflurf

Homework Helper

- 2,440

- 138

Hint what is

$$\sum_{j=0}^m \, A^j$$

what is

$$(I-A)\sum_{j=0}^m \, A^j$$

$$\sum_{j=0}^m \, A^j$$

what is

$$(I-A)\sum_{j=0}^m \, A^j$$

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 809

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 12

- Views
- 1K

- Last Post

- Replies
- 11

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 783

- Last Post

- Replies
- 21

- Views
- 1K

- Last Post

- Replies
- 11

- Views
- 1K