Question

what is solution of |A+B|

Answer 1

i know if
\[|A|≠0\]
then
\[|A+B|=|(I+B A^{-1})A|=|I+B A^{-1}|*|A|\]

if we get
\[C=BA ^{-1}\]
we have

\[|I+C||A|\]

.
if possible i like some expand of it, for example write expand by Eigenvalues |I+C| or ...