Enter all but one of the elements of the original matrix into the calculator to calculate the transpose matrix; this calculator can also evaluate any of the variables given the others are known.
Matrix Transpose Formula
The following formula is used to calculate the transpose of a matrix:
A^T = [a_{ij}]^T = [a_{ji}]Variables:
- A is the original matrix
- AT is the transpose of the matrix
- aij is the element in the i-th row and j-th column of the original matrix
- aji is the element in the j-th row and i-th column of the transpose matrix
To calculate the transpose of a matrix, simply interchange the rows and columns of the original matrix. The element in the i-th row and j-th column of the original matrix becomes the element in the j-th row and i-th column of the transpose matrix.
What is a Matrix Transpose?
A matrix transpose is a fundamental operation in linear algebra which involves flipping a matrix over its diagonal, which starts from the top-left to the bottom-right, thus switching the row and column indices of each element. This means that the element at the ith row and jth column in the original matrix will be placed at the jth row and ith column in the transposed matrix. For instance, if the original matrix is denoted by A, its transpose is usually denoted by A^T or A'. The transpose of a matrix is used in a wide range of mathematical and scientific applications, including simplifying calculations in matrix algebra, solving systems of linear equations, and performing operations in computer graphics.
How to Calculate Matrix Transpose?
The following steps outline how to calculate the Matrix Transpose.
- First, write down the given matrix.
- Next, interchange the rows and columns of the matrix.
- Finally, write down the transposed matrix.
Example Problem:
Use the following matrix as an example problem to test your knowledge.
Given matrix:
1 2 3 4 5 6 7 8 9
Interchanging rows and columns:
1 4 7 2 5 8 3 6 9
Transposed matrix:
1 4 7 2 5 8 3 6 9