ctranspose, '

Complex conjugate transpose

Syntax

B = A'

B = ctranspose(A)

Description

B = A' computes the complex conjugate transpose of A.

B = ctranspose(A) is an alternate way to execute A', but is rarely used. It enables operator overloading for classes.

Examples

Conjugate Transpose of Real Matrix

Create a 4-by-2 matrix.

A = [2 1; 9 7; 2 8; 3 5]

A = 4×2

     2     1
     9     7
     2     8
     3     5

Find the conjugate transpose of A.

B = A'

B = 2×4

     2     9     2     3
     1     7     8     5

The result is a 2-by-4 matrix. B has the same elements as A, but the row and column index for each element are interchanged. When no complex elements are present, A' produces the same result as A.'.

Conjugate Transpose of Complex Matrix

Create a 2-by-2 matrix with complex elements.

A = [0-1i 2+1i;4+2i 0-2i]

A = 2×2 complex

   0.0000 - 1.0000i   2.0000 + 1.0000i
   4.0000 + 2.0000i   0.0000 - 2.0000i

Find the conjugate transpose of A.

B = A'

B = 2×2 complex

   0.0000 + 1.0000i   4.0000 - 2.0000i
   2.0000 - 1.0000i   0.0000 + 2.0000i

The result, B, contains the elements of A with the row and column indices interchanged. The sign of the imaginary part of each number is also switched.

Input Arguments

A — Input array

vector | matrix

Input array, specified as a vector or matrix.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char | string | struct | cell | categorical | datetime | duration | calendarDuration
Complex Number Support: Yes

More About

Complex Conjugate Transpose

The complex conjugate transpose of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal. The operation also negates the imaginary part of any complex numbers.

For example, if B = A' and A(1,2) is 1+1i, then the element B(2,1) is 1-1i.

Tips

• The nonconjugate transpose operator, A.', performs a transpose without conjugation. That is, it does not change the sign of the imaginary parts of the elements.

• For logical or non-numeric inputs, ctranspose and transpose produce the same result.

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 VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

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™.

The ctranspose function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). 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).

Version History

Introduced before R2006a