In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations).

For a given matrix, the transpose of a matrix is obtained by interchanging rows into columns or columns to rows. In this article, we are going to learn the definition of the transpose of a matrix, steps to find the transpose of a matrix, properties and examples with a complete explanation.

Apr 11, 2025 · Transpose of a matrix is a matrix that is obtained by swapping the rows and columns of the given matrix or vice versa, i.e., for the given matrix the elements in rows are interchanged with the elements in columns.

Sep 17, 2022 · The transpose of a matrix is an operator that flips a matrix over its diagonal. Transposing a matrix essentially switches the row and column indices of the matrix.

In linear algebra, the transpose of a matrix is actually an operator that flips a matrix over its diagonal by switching the row and column indices of matrix B and producing another matrix. Transpose of a matrix B is often denoted by either B' or B T. Sometimes, they are also denoted as B tr or B t. If a matrix B is of order m×n, then the ...

Jan 22, 2025 · The transpose of a matrix is a new matrix that is formed by flipping the original matrix over its diagonal. This operation essentially switches the rows and columns of the matrix. If you have a matrix A, the transpose of matrix A is denoted as A T. Example: For a matrix A its transpose A T is given as :

Illustrated definition of Transpose (matrix): Flipping a matrix over its diagonal. The rows and columns get swapped. The symbol is a T placed above and...

The transpose of a matrix is simply a flipped version of the original matrix. We can transpose a matrix by switching its rows with its columns. We denote the transpose of matrix $A$ by $A^T$.

Sep 17, 2022 · Definition \(\PageIndex{1}\): The Transpose of a Matrix Let \(A\) be an \(m\times n\) matrix. Then \(A^{T}\), the transpose of \(A\), denotes the \(n\times m\) matrix given by

Aug 29, 2024 · In linear algebra, the transpose of a matrix is a matrix operation that flips the elements of the given matrix from rows to columns. The symbol of the matrix transpose is A’ or A T . The order of the matrix m × n becomes n × m in the transpose of the matrix.