bookkeeping-transpose#

Purpose#

Transposes a matrix without complex conjugation.

Format#

y = x.'

Parameters#

param x:

Input matrix.

type x:

MxN matrix

Returns#

return y:

Transposed matrix with rows and columns swapped, without conjugation.

rtype y:

NxM matrix

Examples#

x = { 1 2 3,
      4 5 6 };
y = x.';

y =    1.0000000    4.0000000
       2.0000000    5.0000000
       3.0000000    6.0000000

Complex Matrix#

// For complex matrices, .' does NOT conjugate
x = { 1+2i, 3+4i };
y = x.';

// y = { 1+2i,
//       3+4i }
// (imaginary parts remain positive)

// Compare with conjugate transpose:
z = x';

// z = { 1-2i,
//       3-4i }
// (imaginary parts are negated)

Remarks#

For real matrices, .' and ' produce identical results.
For complex matrices, .' preserves the imaginary component while ' conjugates it.