Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a set of Hermitian matrices $A_i$ which are orthonormal in the Frobenius inner product $\langle A_i,A_j\rangle=\mathrm{Tr}(A_i^{\dagger}A_j)=\delta_{ij}$, and I know there exists a basis in which the orthonormality and Hermiticity are preserved but all matrices are positive definite. Expressing the matrices in the positive definite basis as

$$ B_i=\sum_{\gamma} c_{\gamma i}A_{\gamma},$$

the Hermiticity and orthonormality requirements require that $c$ be an orthogonal matrix. Is there a simple means of finding the transformation matrix $c$?

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.