Series or Tensors!!?

[mos5250]

Hi all;

Can anybody Help me to solve the problem, i've encountered recently... please...
thanks in advance...

i wanna solve the last equality (for C):

. . . . .\(\displaystyle \large{A\, =\, }\)\(\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda_k\, V_k\, V_k^T}\)

. . . . .\(\displaystyle \large{B\, =\, }\)\(\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda^{'}_k\, U_k\, U_k^T}\)

. . . . .\(\displaystyle \large{C\, =\, A\, B^{-1}}\)

 

[Deleted member 4993]

Hi all;

Can anybody Help me to solve the problem, i've encountered recently... please...
thanks in advance...

i wanna solve the last equality (for C):

. . . . .\(\displaystyle \large{A\, =\, }\)\(\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda_k\, V_k\, V_k^T}\)

. . . . .\(\displaystyle \large{B\, =\, }\)\(\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda^{'}_k\, U_k\, U_k^T}\)

. . . . .\(\displaystyle \large{C\, =\, A\, B^{-1}}\)

You are given B as a series.

How would you express B^-1 as a series?