How to Find the Transpose of a Matrix?
Transpose of any matrix can easily be found by changing the values in the rows with the values in the columns. Let’s take an example to understand this in detail.
For any matrix A2×3, the order is 2×3 which means it has 2 rows and 3 columns.
A = [Tex] \begin{bmatrix} a & b & c\\ x & y & z \end{bmatrix} [/Tex]
The transpose of matrix A is At of the order 3×2 having 3 rows and 2 columns. In the transpose matrix elements of the first row of the given matrix are changed with the first column of the transpose matrix. Similarly, the elements of the second row of the given matrix A are swapped with the second column of the new matrix At and so on till the whole matrix is swapped.
At = [Tex]\begin{bmatrix} a & x \\ b & y \\ c & z \end{bmatrix} [/Tex]
Transpose of a Matrix
Transpose of a matrix is a very common method used for matrix transformation in linear algebra. Transpose of a matrix is obtained by interchanging the rows and columns of the given matrix or vice versa. Transpose of a matrix can be utilized to obtain the adjoint and inverse of the matrices.
Before learning about the details of the transpose of a matrix let’s first learn about “What is a matrix?”. A matrix is nothing but the representation of the set of data in the rectangular array format. In a matrix, data is arranged in specific rows and columns. Various types of matrices exist in Mathematics and are presented in the order of rows × columns. Let’s take an example of the matrix of order 3 × 2 (say A).
A = [Tex]\begin{bmatrix}1 & 2\\ 3 & 4\\ 5 & 6\end{bmatrix} [/Tex]
In this article, we will learn about the transpose of a matrix, its types, properties, symbols, and order, how to find the transpose of a matrix, and examples of it.
Table of Content
- What is a Matrix?
- Types of Matrices
- What is Transpose of a Matrix?
- Symbol of Transpose Matrix | Transpose Notation
- Order of Transpose Matrix
- How to Find the Transpose of a Matrix?
- Transpose of Row and Column Matrix
- Transpose of Horizontal and Vertical Matrices
- Transpose of a Symmetric Matrix
- Transpose of a Diagonal Matrix
- Transpose of a Transposed Matrix
- Transpose of a Square Matrix
- Transpose of a 3 × 3 Matrix
- Determinant of Transpose of a Matrix
- Transpose of a Matrix Properties