Matrix transpose
Page Navigation:
Definition.
Transposing the matrix is an operation on the matrix in which its rows and columns are swapped:aTij = aji
Properties of transpose matrix
- If matrix A has a size of n×m, then the transposed matrix AT has a size of m×n;
- (AT)T = A;
- (k · A)T = k · AT;
- (A + B)T = AT + BT;
- (A · B)T = BT · AT.
Examples of matrix transpose
Example 1.
Find the transposed matrix AT for matrix
| A = |  |
4 | 2 |  |
. |
| 9 | 0 |
Solution:
| AT = | |
4 | 9 | |
| 2 | 0 |
Example 2
Find the transposed matrix AT for matrix
| A = | |
2 | 1 | |
. |
| -3 | 0 | ||||
| 4 | -1 |
Solution:
| AT = | |
2 | -3 | 4 | |
| 1 | 0 | -1 |
Example 3
Find the transposed matrix AT for matrix
| A = | |
2 | -3 | 4 | |
. |
| 1 | 0 | -1 |
Solution:
| AT = | |
2 | 1 | |
| -3 | 0 | |||
| 4 | -1 |
MatrixMatrix Definition. Main informationSystem of linear equations - matrix formTypes of matricesMatrix scalar multiplicationAddition and subtraction of matricesMatrix multiplicationTranspose matrixElementary matrix operationsDeterminant of a matrixMinors and cofactors of a matrixInverse matrixLinearly dependent and independent rowsRank of a matrix
Add the comment