# [Numpy-discussion] Question about complex variables

Paulo J. S. Silva rsilva at ime.usp.br
Wed May 12 03:46:05 CDT 2004

```Karthik,

You are making a common mistake. In Mathematics, the "transpose" of a
matrix is just the matrix with the axis transposed like numarray/numeric
does. What you called transpose is actually the "adjoint" or "conjugate
transpose" of a matrix. Actually, this last operation (the adjoint) is
the most interesting one in Linear Algebra/Functional Analysis. For more
details take a look at:

http://en.wikipedia.org/wiki/Conjugate_transpose
http://en.wikipedia.org/wiki/Transpose

In the reals both operations coincide, thus the confusion. This is the
reason why matlab can use the same symbol for both operations.

Now, enough Mathematics, let's go to numarray. To get the adjoint of a
matrix A in numarray, you can simply do:

conjugate(transpose(A))

If you want, you may define a function named adjoint to perform the
above operations.

Note that this creates a new matrix, not only a new view of the original
matrix like "transpose" function in numarray.

Hope it helps,

Paulo
--
Paulo José da Silva e Silva
Professor Assistente do Dep. de Ciência da Computação
(Assistant Professor of the Computer Science Dept.)
Universidade de São Paulo - Brazil

e-mail: rsilva at ime.usp.br          Web: http://www.ime.usp.br/~rsilva

Teoria é o que não entendemos o    (Theory is something we don't)
suficiente para chamar de prática. (understand well enough to call)
(practice)

```