What Is A Matrix Transpose

The transpose of a matrix can be defined as an operator which can switch the rows and column indices of a matrix i e.

What is a matrix transpose.

For example if you transpose a n x m size matrix you ll get a new one of m x n dimension. It flips a matrix over its diagonal. Taking a transpose of matrix simply means we are interchanging the rows and columns. Let s understand it by an example what if looks like after the 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. Transpose a matrix means we re turning its columns into its rows. Dimension also changes to the opposite. Matrix transposes are a neat tool for understanding the structure of matrices.

But the original matrix is unitary. This matrix is symmetric and all of its entries are real so it s equal to its conjugate transpose. There is not computation that happens in transposing it. Features you might already know about matrices such as squareness and symmetry affect the transposition results in obvious ways.

Transpose is generally used where we have to multiple matrices and their dimensions without transposing are not amenable for multiplication. Transposition also serves purposes when expressing vectors as matrices or taking the products of vectors. That is it switches the row and column indices of the matrix a by producing another matrix often denoted by at among other notations. The transpose of a matrix was introduced in 1858 by the british mathematician arthur cayley.

Each i j element of the new matrix gets the value of the j i element of the original one. In linear algebra the transpose of a matrix is an operator which flips a matrix over its diagonal. The algorithm of matrix transpose is pretty simple.