Transposed Matrix

The transposed matrix calculator online is a tool that allows you to exchange rows for columns of a matrix automatically. Just select the size of the matrix from the available sizes and click the Calculate button to get the transpose of that matrix.

If you want to know everything about the transposed matrixRead on and we will tell you all about this type of matrix used in the world of mathematics, physics and other disciplines.

What is a transposed matrix

Transposed matrix formula

The transpose of a matrix is the one in which rows have been exchanged for columns. This is an operation that does not require any additional calculations, so it is an operation that will only take a few seconds.

It should be noted that when transposing a matrix, we add a small T in the upper right part, so that visually it can be seen as follows (A)t.

How to make a transposed matrix

As we have seen in the previous point, make a transposed matrix consists of exchanging rows for columns. To make it clearer, let's see it with a practical example like the following one:

Example of transposed matrix

The only difficulty calculate the transposed matrix is not to make a mistake when changing the rows by columns and that we make a mistake in any number. Otherwise, it is very easy to do.

Properties of the transposed matrix

Transposed matrix

Below you will find the main properties of the transposed matrix for you to take into account when solving mathematical problems with them:

  • (At)t=A: this means that if we transpose a transposed matrixwe are left with the starting matrix.
  • (A + B)t = At + Bt : the transpose of the sum of matrices is equal to the sum of the transposed matrix of each of the matrices.
  • (AB)t = BtAt: the transpose of the product of two matrices is equal to the product of the transpose matrix of each of the matrices.
  • (rA)t = rAt: yes a scalar number multiplies a matrixThe order in which we do the transposed matrix is irrelevant since we will obtain the same result.

Transposed matrix in Excel

There are two ways to transpose a matrix in Excel although depending on which one we choose, we will have a referenced result or not.

What does this mean? That if we choose the non-referenced form, when we make changes in the matrix, the transposed one will not have those changes applied instantaneously while in the other form, all the modifications we make will be automatically seen in the transposed matrix.

Let's see how each one is done.

Unreferenced transposed matrix

Transposed matrix in Excel

In this case, we only have to type the elements of the matrix, select the range of data and copy them to the clipboard (CTRL+C or CMD+C if you use Mac).

Next, select an empty cell in the spreadsheet, go to the paste options and select the Transpose" option. After pressing it, you will see that the data has been transposed.

The disadvantage of this method is that if we modify the original matrix, the transpose is unchanged. To solve this, let's look at the method referenced below.

Transpose function in Excel

Transpose function in Excel

This second method is the one that allows us to transpose data in Excel automatically and bindingly, so that if we make changes in the original matrix, the transposed one will also have those changes applied at the time.

To do this, type the elements of the matrix and when you have done so, searches for a range of blank cells matching the number of cells that are in the original array. That is, if we have an original array of 2×4 cells, we must select a range of 4×2 cells for the transpose function to be applied correctly.

When you have that range of empty cells selected, write the following function making sure that between the parentheses, you have selected the range of data in which the starting matrix is located.

=TRANSPONER()

Then, press CTRL+SHIFT+DELETE on your keyboard and you will see that the following is displayed in Excel the transposed matrix.

Determinant of a transposed matrix

The determinant of a matrix is equal to the determinant of its transpose such that:

Determinant of (A) = Determinant (A)t

It is important to remember that only the determinant of square matrices can be calculatedthat is, whose number of rows is equal to the number of columns. If you want, here you can learn more about how to calculate the following types of determinants:

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