What Is A Matrix Transpose

Let s say you have original matrix something like x 1 2 3 4 5 6 in above matrix x we have two columns containing 1 3 5 and 2 4 6.

What is a matrix transpose. Let s understand it by an example what if looks like after the transpose. Dimension also changes to the opposite. Transpose a matrix means we re turning its columns into its rows. Each i j element of the new matrix gets the value of the j i element of the original one.

Transposition also serves purposes when expressing vectors as matrices or taking the products of vectors. The transpose of a matrix can be defined as an operator which can switch the rows and column indices of a matrix i e. 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 at among other notations.

A new matrix is obtained the following way. It flips a matrix over its diagonal. Transpose is generally used where we have to multiple matrices and their dimensions without transposing are not amenable for multiplication. This matrix is symmetric and all of its entries are real so it s equal to its conjugate transpose.

The transpose of a matrix was introduced in 1858 by the british mathematician arthur cayley. Matrix transposes are a neat tool for understanding the structure of matrices. How to calculate the transpose of a matrix. The algorithm of matrix transpose is pretty simple.

For example if you transpose a n x m size matrix you ll get a new one of m x n dimension. But the original matrix is unitary. Features you might already know about matrices such as squareness and symmetry affect the transposition results in obvious ways.