Transpose in matlab

Transpose in matlab DEFAULT

Transpose Matrix Matlab

Transpose Matrix Matlab

Introduction to Transpose Matrix Matlab

In this article, we will learn about Transpose Matrix Matlab. If output matrix rows are equal to input columns and output matrix columns are equal to rows of the input matrix then the output matrix is called ‘transpose of the matrix’. This ‘T’ represents the transpose of the matrix. Let us consider there are two matrices one is the input matrix ‘I’ and the second is the output matrix ‘O’. A number of rows of the input matrix are ‘Irow’. The number of columns in the input matrix is ‘Idol’ and the number of rows in the output matrix is ‘Orow’. Number of columns in output matrix is ‘Ocol’ then Transpose of matrix satisfies two conditions which are Icol=Orow and Irow=Ocol.(rows of input matrix =column of output matrix and columns of input matrix=rows of output matrix)

How We Can Do Transpose Matrix in Matlab?

There are two ways to find out transpose of a matrix in Matlab which are:

  1. By Using Operator
  2. By Using Command

1. By Using Operator

In this method, the dot operator is used to finding the transpose of the matrix (. ’). This is one of the easiest and simple methods for transpose. The only limit of this method is there are high chances of syntax error because of the operator.

Syntax:

Steps:

  • Accept input matrix by using square matrix (Input = [ 23 , 32 , 11 ; 22 3 2 ; 16 39 21 ; 32 4 1 ]
  • Apply the operator on the input matrix ( output matrix=input matrix.’)
  • Display the output matrix.

2. By Using Command

In this method, ‘transpose’ command is used to find out the transpose of the matrix. This method is less complex and easy to implement as compared to the previous method. And there are fewer chances of error at the time of implementation.

Syntax:

Steps:

  • Accept input matrix by using square matrix (Input = [ 23 , 32 , 11 ; 22 3 2 ; 16 39 21 ; 32 4 1 ]
  • Apply command on input matrix ( output matrix = transpose (input matrix))
  • Display output matrix.

Examples for Transpose Matrix Matlab

Following are the examples implement the matrix Matlab:

Example #1

Let us consider the input matrix as mat1;
Code:

The following table illustrates the Matlab code for example 1 by using the operator.

Matlab EditorCommand Window(output)

mat1 = [ 23 , 32 , 11 ; 22 3 2 ; 16 39 21 ; 32 4 1 ] mat3 = mat1 . ‘

mat1 =

23    32    11

22     3     2

16    39    21

32     4     1

mat3 =

23    22    16    32

32     3    39     4

11     2    21     1

Output:

using the operator

The following table illustrate the Matlab code for example 1 by using transpose command:

Matlab EditorCommand Window(output)
mat1 = [ 23 , 32 , 11 ; 22 3 2 ; 16 39 21 ; 32 4 1 ]

mat2=transpose(mat1)

mat1 =

23    32    11

22     3     2

16    39    21

32     4     1

mat2 =

23    22    16    32

32     3    39     4

11     2    21     1

Transpose Matrix Matlab - 2

Example #2

Let us assume input matrix is mat1 in form of the magic command.

The following table illustrates the Matlab code for example 1 by using a transpose operator.

Matlab EditorCommand Window (Output)

mat1 = magic(4)

mat2 = mat1.’

mat1 =

16     2     3    13

5    11    10     8

9     7     6    12

4    14    15     1

mat2 =

16     5     9     4

2    11     7    14

3    10     6    15

13     8    12     1

transpose operator

Following table illustrate the Matlab code for example 2 by using transpose command.

Matlab EditorCommand Window ( Output )
mat1 = magic ( 4 )%no 4 represents no of rows and columns%

mat2=transpose(mat1)

mat1 =

16     2     3    13

5    11    10     8

9     7     6    12

4    14    15     1

mat2 =

16     5     9     4

2    11     7    14

3    10     6    15

13     8    12     1

transpose command

Example #3

Now consider one input matrix with complex numbers.

Matlab EditorCommand Window ( Output )
mat1 = [ 1 – 3 i , 4  + 4 i , 8 , 2 – 5 i ; 5  , 3 , 6 + 8 i , 4 + 4 i ; i , 7 + 8 i , 9 + 9 i , 10]

mat2=mat1.’

mat1 =

1.0000 – 3.0000i   4.0000 + 4.0000i   8.0000 + 0.0000i   2.0000 – 5.0000i

5.0000 + 0.0000i   3.0000 + 0.0000i   6.0000 + 8.0000i   4.0000 + 4.0000i

0.0000 + 1.0000i   7.0000 + 8.0000i   9.0000 + 9.0000i  10.0000 + 0.0000i

mat2 =

1.0000 – 3.0000i   5.0000 + 0.0000i   0.0000 + 1.0000i

4.0000 + 4.0000i   3.0000 + 0.0000i   7.0000 + 8.0000i

8.0000 + 0.0000i   6.0000 + 8.0000i   9.0000 + 9.0000i

2.0000 – 5.0000i   4.0000 + 4.0000i  10.0000 + 0.0000i

 complex numbers

Matlab EditorCommand Window ( Output )
mat1=[1-3i,4+4i,8,2-5i;5,3,6+8i,4+4i;i,7+8i,9+9i,10]

mat2=transpose(mat1)

mat1 =

1.0000 – 3.0000i   4.0000 + 4.0000i   8.0000 + 0.0000i   2.0000 – 5.0000i

5.0000 + 0.0000i   3.0000 + 0.0000i   6.0000 + 8.0000i   4.0000 + 4.0000i

0.0000 + 1.0000i   7.0000 + 8.0000i   9.0000 + 9.0000i  10.0000 + 0.0000i

mat2 =

1.0000 – 3.0000i   5.0000 + 0.0000i   0.0000 + 1.0000i

4.0000 + 4.0000i   3.0000 + 0.0000i   7.0000 + 8.0000i

8.0000 + 0.0000i   6.0000 + 8.0000i   9.0000 + 9.0000i

2.0000 – 5.0000i   4.0000 + 4.0000i  10.0000 + 0.0000i

Transpose Matrix Matlab - 6

Conclusion

Transpose of the matrix is one of the important terminologies used in matrix manipulations. In this section we have seen how to find out transpose of a matrix by using two methods one is by using the operator and the other one is by using transpose command. Along with the different methods, we have seen different matrices as input to check the system (real numbers, random numbers, and complex numbers).

Recommended Articles

This is a guide to Transpose Matrix Matlab. Here we discuss the examples to implement the transpose matrix Matlab by using operator and command. You can also go through our other related articles to learn more –

  1. Colors in Matlab
  2. Scatter Plots in Matlab
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  5. Guide to Working of Gradient in Matlab
  6. Guide to Various Examples of Matlab Inverse Function
Sours: https://www.educba.com/transpose-matrix-matlab/

transpose, .'

Main Content

Description

Examples

Transpose of Real Matrix

Create a -by- matrix, the elements of which represent real numbers.

syms x y real A = [x x x; y y y]
A = [ x, x, x] [ y, y, y]

Find the nonconjugate transpose of this matrix.

ans = [ x, y] [ x, y] [ x, y]

If all elements of a matrix represent real numbers, then its complex conjugate transform equals its nonconjugate transform.

ans = 3×2 logical array 1 1 1 1 1 1

Transpose of Complex Matrix

Create a -by- matrix, the elements of which represent complex numbers.

syms x y real A = [x + y*i x - y*i; y + x*i y - x*i]
A = [ x + y*1i, x - y*1i] [ y + x*1i, y - x*1i]

Find the nonconjugate transpose of this matrix. The nonconjugate transpose operator, , performs a transpose without conjugation. That is, it does not change the sign of the imaginary parts of the elements.

ans = [ x + y*1i, y + x*1i] [ x - y*1i, y - x*1i]

For a matrix of complex numbers with nonzero imaginary parts, the nonconjugate transform is not equal to the complex conjugate transform.

isAlways(A.' == A','Unknown','false')
ans = 2×2 logical array 0 0 0 0

Input Arguments

collapse all

— Input
number | symbolic number | symbolic scalar variable | symbolic matrix variable | symbolic function | symbolic expression | symbolic vector | symbolic matrix | symbolic array

Input, specified as a number, or a symbolic number, scalar variable, matrix variable (since R2021a), function, expression, or vector, matrix, or array of symbolic scalar variables.

More About

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Nonconjugate Transpose

The nonconjugate transpose of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal. The diagonal elements themselves remain unchanged. This operation does not affect the sign of the imaginary parts of complex elements.

For example, if and is , then the element is .

Introduced before R2006a

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Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

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transpose, .'

Main Content

Description

example

returns the nonconjugate transpose of , that is, interchanges the row and column index for each element. If contains complex elements, then does not affect the sign of the imaginary parts. For example, if is and , then the element is also .

is an alternate way to execute and enables operator overloading for classes.

Examples

collapse all

Real Matrix

Create a matrix of real numbers and compute its transpose. has the same elements as , but the rows of are the columns of and the columns of are the rows of .

A = 4×4 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
B = 4×4 16 5 9 4 2 11 7 14 3 10 6 15 13 8 12 1

Complex Matrix

Create a matrix containing complex elements and compute its nonconjugate transpose. contains the same elements as , except the rows and columns are interchanged. The signs of the imaginary parts are unchanged.

A = [1 3 4-1i 2+2i; 0+1i 1-1i 5 6-1i]
A = 2×4 complex 1.0000 + 0.0000i 3.0000 + 0.0000i 4.0000 - 1.0000i 2.0000 + 2.0000i 0.0000 + 1.0000i 1.0000 - 1.0000i 5.0000 + 0.0000i 6.0000 - 1.0000i
B = 4×2 complex 1.0000 + 0.0000i 0.0000 + 1.0000i 3.0000 + 0.0000i 1.0000 - 1.0000i 4.0000 - 1.0000i 5.0000 + 0.0000i 2.0000 + 2.0000i 6.0000 - 1.0000i

Input Arguments

collapse all

— Input array
vector | matrix

Input array, specified as a vector or matrix.

Data Types: | | | | | | | | | | | | | | | | | |
Complex Number Support: Yes

Tips

  • The complex conjugate transpose operator, , also negates the sign of the imaginary part of the complex elements in .

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Thread-Based Environment
Run code in the background using MATLAB® or accelerate code with Parallel Computing Toolbox™ .

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Introduced before R2006a

You have a modified version of this example. Do you want to open this example with your edits?

You clicked a link that corresponds to this MATLAB command:

Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

Select web site

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Transpose in matlab

It is due to how shapes the vector. In this case reshapes the 1-by-16 vector into a 4-by-4 array by traversing column-wise. In this case, you must take the transpose or complex-conjugate transpose to make each column effectively be a row, similar to rotating the matrix. Visually:

Test Script:

Before Transposing → :

After Complex-Conjugate Transposing → :


Extension:

For complex numbers does more than transposing. It also takes the complex conjugate.

Code Snippet: Taking the complex-conjugate and transposing

Returns:

ans =

5.0000 - 2.0000i


Code Snippet: Taking the transpose

Returns:

ans =

5.0000 + 2.0000i

Ran using MATLAB R2019b

Sours: https://stackoverflow.com/questions/64852025/transpose-in-matlab

Matlab transpose in

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How to Import Excel Data into MATLAB

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