Matrix

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Matrix Transpose Result

What is Matrix Transpose?

How to use Matrix Transpose Calculator?

What is matrix transpose used for?

When is matrix transpose equal to original matrix?

When is matrix transpose equal to its inverse?

Are eigen values of a matrix and its transpose same?

Are transpose of inverse matrix and inverse of transpose matrix same?

Matrix Transpose Example #1

Matrix Transpose Example #2

Matrix Transpose Example #3

Matrix transpose is a matrix transformation method of converting rows into columns and columns into rows. The transpose of a matrix X is denoted by X^T.

Matrix transpose calculator (above) can be used to find the transpose of a matrix. You can increase or decrease the number of rows and columns of a matrix using the + and - buttons.

The matrix input box will be updated to according to number of rows and columns you select.

Fill the values in the input box and click on the 'Transpose' button to find the transpose of the matrix.

You can also enter non-numeric values like x, y, a, b, etc. in the matrix input box. The calculator will treat them as variables and will show the transpose of the matrix with variables.

Matrix transpose is mostly used when two matrices are not in the same order (dimensions). So, one of the matrix is transposed to match the order of the other matrix.

There is no computation involved in matrix transpose, its just changing rows into columns and columns into rows.

A matrix transpose which is equal to its original matrix is called symmetric matrix

A matrix is equal to its transpose, if it is a square matrix

A matrix is equal to its inverse, if it is a orthogonal matrix. Orthogonal matrix is a matrix, which when multiploed by its transpose gives identity matrix.

The eigen values of a matrix and its transpose are same.

Lets say A is a matrix, then (A^-1)^T = (A^T)^-1.

Which means yes, The transpose of inverse matrix is equal to inverse of transpose matrix.

Lets say we have a matrix C = [ [ 23 34 54 ] [ 34 46 23 ] [ 87 65 23 ] ]

The transpose of matrix C is C^T = [ [23 34 87] [34 46 65 ] [54 23 23 ] ]

Take matrix G = [ [2 4 6] [3 6 1] [7 2 9] ]

The transpose of matrix G is G^T = [ [2 3 7] [4 6 2] [6 1 9] ]

Take matrix H = [ [ 7 28 323 -54 ] [ -5 65 23 x ] [9 10 b -1/2] ]

The transpose of matrix H is H^T = [ [7 -5 9] [28 65 10] [323 23 b] [-54 x -1/2] ]

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