Use the Einstein summation convention, with repeated component indices summed. The following three expressions are listed separately below. For cyclic invariance of the trace,
(1)
where the middle equality commutes scalar entries, not the matrices themselves. If is invertible, this gives
(2)
This is similarity invariance of trace.
Taking the diagonal sum of the matrix product gives
(1)
Both repeated indices are summed from one to .
Apply row-column matrix multiplication twice:
(1)
The indices are free, while are summed.
The identity matrix has entries given by the Kronecker delta, so
(1)
Each of the diagonal entries is one.

Ancestors (12)

  1. 10
  2. Paper 1
  3. 2001
  4. Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
  5. Mathematics course of the year 1 of the natural sciences course of the University of Cambridge
  6. Year 1 of the natural sciences course of the University of Cambridge
  7. Year of the natural sciences course of the University of Cambridge
  8. Natural sciences course of the University of Cambridge
  9. Course of the University of Cambridge
  10. University of Cambridge
  11. List of universities
  12. Home

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version