# Transpose operator homework help

If you have opted for or are planning to take up a mathematics course on campus. You will definitely come across matrices. A matrix is a two-dimension array from which mathematical computations such as addition, subtraction, multiplications, and division can be done. An example of a matrix is the one shown below.

The numbers or symbols of the matrix are known as elements, the vertical elements are the column, and the horizontal are the rows. We define the size of a matrix as the number of columns and rows it contains. For example, an M X N matrix contains M and N dimensions. The number of rows and columns that a matrix can contain can be infinite, while it is possible to contain a matrix with one column or row. Such a matrix is called a column vector and a row vector, respectively. If the matrix has the same number of rows and columns, it is known as a square matrix. An example shown above is a matrix with three rows. An empty matrix does not have any element.

Howsoever, simple the idea of matrices may sound, they have applications in real life. Examples are in robotics and are the common way of storing data for most organizations.

### Transposition operator

A transpose operator of a matrix is defined as the operator that flips a matrix over its diagonal. It changes the row of a matrix to be it’s diagonal. In mathematics, the transpose of a matrix denoted with a superscript t on the matrix name. For a matrix A above, its transpose is denoted by A^{T}or A^{t}.

### How to find the transpose of a matrix.

We shall use Matrix A to demonstrate this example.

- The first step is reflecting the matrix over its diagonal.
- Write the columns of A as rows of A
^{T} - Write rows of A as columns of A
^{T}

The final result of A^{T} is given below.

Transpose operator for a vector.

A vector is a one-dimensional array. In some cases, we can say a vector is simply a single row or column matrix.

Having found the transpose of the matrix, we can do all the mathematical manipulations, including multiplication, division, addition, subtraction, and even finding the determinant.

### Properties of the transpose operator.

Let us take two arbitrary matrices A and B, and we assume that they have a transpose. Below are the common properties of a transpose matrix.

- (A
^{T})^{T}= A - A
^{T}+B^{T}= (A+B)^{T}

The addition transpose of matrices A and B is the same as adding matrix A and B then transposing the answer. The same can be said in the multiplication of transpose matrices.

- The determinant of the transpose of matrix A is the same as the determinant of matrix A.

Transpose Operator in Matlab.

Matlab is one of the trusted statistical computing software capable of solving any mathematical problem. A large number of universities and colleges have incorporated a course on Matlab and they offer assignments related to Matlab. The assignments improve their knowledge of the software. With Matlab, you can easily create a matrix and find the transpose using different functions. The simplest function in Matlab is the transpose.

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