# pagectranspose

Page-wise complex conjugate transpose

Since R2020b

## Description

example

Y = pagectranspose(X) applies the complex conjugate transpose to each page of N-D array X. Each page of the output Y(:,:,i) is the conjugate transpose of the corresponding page in X, as in X(:,:,i)'.

## Examples

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Create a 3-D complex array A, and then use pagectranspose to find the complex conjugate transpose of each page of the array.

r = repelem(1:3,3,1);
A = cat(3,r,2*r,3*r);
A = A + 1i
A =
A(:,:,1) =

1.0000 + 1.0000i   2.0000 + 1.0000i   3.0000 + 1.0000i
1.0000 + 1.0000i   2.0000 + 1.0000i   3.0000 + 1.0000i
1.0000 + 1.0000i   2.0000 + 1.0000i   3.0000 + 1.0000i

A(:,:,2) =

2.0000 + 1.0000i   4.0000 + 1.0000i   6.0000 + 1.0000i
2.0000 + 1.0000i   4.0000 + 1.0000i   6.0000 + 1.0000i
2.0000 + 1.0000i   4.0000 + 1.0000i   6.0000 + 1.0000i

A(:,:,3) =

3.0000 + 1.0000i   6.0000 + 1.0000i   9.0000 + 1.0000i
3.0000 + 1.0000i   6.0000 + 1.0000i   9.0000 + 1.0000i
3.0000 + 1.0000i   6.0000 + 1.0000i   9.0000 + 1.0000i

B = pagectranspose(A)
B =
B(:,:,1) =

1.0000 - 1.0000i   1.0000 - 1.0000i   1.0000 - 1.0000i
2.0000 - 1.0000i   2.0000 - 1.0000i   2.0000 - 1.0000i
3.0000 - 1.0000i   3.0000 - 1.0000i   3.0000 - 1.0000i

B(:,:,2) =

2.0000 - 1.0000i   2.0000 - 1.0000i   2.0000 - 1.0000i
4.0000 - 1.0000i   4.0000 - 1.0000i   4.0000 - 1.0000i
6.0000 - 1.0000i   6.0000 - 1.0000i   6.0000 - 1.0000i

B(:,:,3) =

3.0000 - 1.0000i   3.0000 - 1.0000i   3.0000 - 1.0000i
6.0000 - 1.0000i   6.0000 - 1.0000i   6.0000 - 1.0000i
9.0000 - 1.0000i   9.0000 - 1.0000i   9.0000 - 1.0000i

## Input Arguments

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Input array, specified as a multidimensional array.

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

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### Array Pages

Page-wise functions like pagectranspose operate on 2-D matrices that have been arranged into a multidimensional array. For example, the elements in the third dimension of a 3-D array are commonly called pages because they stack on top of each other like pages in a book. Each page is a matrix that the function operates on.

You can also assemble a collection of 2-D matrices into a higher dimensional array, like a 4-D or 5-D array, and in these cases pagectranspose still treats the fundamental unit of the array as a 2-D matrix that the function operates on, such as X(:,:,i,j,k,l).

The cat function is useful for assembling a collection of matrices into a multidimensional array, and the zeros function is useful for preallocating a multidimensional array.

## Tips

• The page-wise complex conjugate transpose is equivalent to permuting the first two dimensions of the array with permute(conj(X),[2 1 3:ndims(X)]).

## Version History

Introduced in R2020b