transpose, .'

Symbolic matrix transpose

Syntax

``A.'``
``transpose(A)``

Description

example

``A.'` computes the nonconjugate transpose of `A`.`
````transpose(A)` is equivalent to `A.'`.```

Examples

Transpose of Real Matrix

Create a `2`-by-`3` 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.

`A.'`
```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.

`isAlways(A' == A.')`
```ans = 3×2 logical array 1 1 1 1 1 1```

Transpose of Complex Matrix

Create a `2`-by-`2` 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, `A.'`, performs a transpose without conjugation. That is, it does not change the sign of the imaginary parts of the elements.

`A.'`
```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, 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.

For example, if `B = A.'` and `A(3,2)` is `1+1i`, then the element `B(2,3)` is `1+1i`.