Transposed Matrix
The transposed matrix calculation tool is a tool that allows you to easily find the "transposed matrix" of a specified matrix. With this tool, you can simply enter numbers into the matrix and the calculation result of the transposed matrix will be automatically displayed.
Results of transposed matrix calculation
How to use
- Enter a value in "Matrix".
- "Transposed matrix" will be calculated automatically.
What is a transposed matrix?
A transposed matrix is a new matrix in which the "rows" and "columns" of a matrix are swapped.
The transposed matrix of a matrix A is written as AT.
Definition
The transpose matrix AT of a matrix A can be obtained by arranging the elements as follows:
Original matrix:
A =
[ 1 2 ]
[ 3 4 ]
Transposed matrix:
AT =
[ 1 3 ]
[ 2 4 ]
Features
- Swap rows and columns: The rows of the original matrix become the columns of the transposed matrix.
- Symmetric matrices: For a symmetric matrix, A = AT.
- Change of dimensions: If the original matrix is m × n, then the transpose is n × m.
Example
Original matrix:
B = [ 1 2 3 ]
[ 4 5 6 ]
Transposed matrix:
BT = [ 1 4 ]
[ 2 5 ]
[ 3 6 ]
How to calculate the transpose of a matrix
The steps to calculate the transpose of a matrix are as follows.
- Identify the elements of the original matrix.
- Move the rows of the original matrix to the columns of the new matrix.
- Move the columns of the original matrix to the rows of the new matrix.
Example:
Original matrix:
C =
[ 7 8 9 ]
[ 10 11 12 ]
Calculation procedure:
- First row: [ 7, 8, 9 ] → First column of the transposed matrix.
- Second row: [ 10, 11, 12 ] → Second column of the transposed matrix.
Transposed matrix:
CT = [ 7 10 ]
[ 8 11 ]
[ 9 12 ]
Notes
This tool is available for free.
※This program is created and confirm the operation in PHP8.1.22.
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