transpose, .'

Symbolic matrix transpose

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Syntax

A.'
transpose(A)

Description

A.' computes the nonconjugate transpose of A.

example

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

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

More About

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Version History

Introduced before R2006a

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See Also

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