What is matrix transpose?
- It is a fundamental operation in linear algebra that involves flipping a matrix on its diagonal.
- This creates a new matrix where the rows of the original matrix become columns, and vice versa.
Example:
Original Matrix:
A = | 1 2 3 |
| 4 5 6 |
| 7 8 9 |
Transposed matrix (A^t):
A^t = | 1 4 7 |
| 2 5 8 |
| 3 6 9 |
key points:
- The dimensions of the transposed matrix are reversed: rows become columns, and columns become rows.
- Elements on the main diagonal (from top-left to bottom-right) remain in the same position.
- The notation for transpose is usually a superscript T (e.g. A^T).
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