0
$\begingroup$

Let $V$ be a finite dimensional vector space, with some choice of basis $\{e_i\}_{i \in I}$. With respect to an idempotent bijection $B:I \to I$, define a bilinear form by $$ g = \sum_{i=1}^N \lambda_{i} e^i \otimes e^{B(j)}, $$ where $\{e^i\}_{i \in I}$ is the dual basis of $V^*$. Moreover, assume that $\lambda_i \neq \lambda_{I(i)}$, implying that $g$ is not a symmetric form. I would like to know if such a $g$ has a name, and if anyone has previously considered such objects.

$\endgroup$
2
  • $\begingroup$ Do you mean $B(i)$ rather than $I(j)$ in the superscript? And is $I=\lbrace 1, \dots, N \rbrace$? $\endgroup$
    – MTS
    Jul 26, 2013 at 18:29
  • $\begingroup$ . . . and yes $I=\{1,\ldots, N\}$. $\endgroup$ Jul 26, 2013 at 18:43

1 Answer 1

2
$\begingroup$

You may find the following link helpful: http://en.wikipedia.org/wiki/Generalized_permutation_matrix

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.