- #1
csnsc14320
- 57
- 1
Homework Statement
Give the basis and dimension of the set of all 2x2 complex symmetric matrices.
Homework Equations
The Attempt at a Solution
I know that if the coefficients were real, then I could just have the basis
[tex]
\left(
\begin{array}{cc}
1 & 0\\
0 & 0
\end{array}
\right),
\left(
\begin{array}{cc}
0 & 1\\
1 & 0
\end{array}
\right),
\left(
\begin{array}{cc}
0 & 0\\
0 & 1
\end{array}
\right)
[/tex]
but if the entries of the matrix can be in the form of a+bi, where a and b are real numbers, do I need three SEPARATE matrices with "i" coefficients or can i combine them somehow?
i.e., extend the dimension to 6 by:
[tex]
\left(
\begin{array}{cc}
i & 0\\
0 & 0
\end{array}
\right)
\left(
\begin{array}{cc}
0 & i\\
i & 0
\end{array}
\right)
\left(
\begin{array}{cc}
0 & 0\\
0 & i
\end{array}
\right)
[/tex]
and thus my dimension would be 6?