Series or Tensors!!?

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mos5250

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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):

. . . . .A = \displaystyle \large{A\, =\, }∑k=1N λk Vk VkT\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda_k\, V_k\, V_k^T}

. . . . .B = \displaystyle \large{B\, =\, }∑k=1N λk′ Uk UkT\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda^{'}_k\, U_k\, U_k^T}

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

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mos5250 said:
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):

. . . . .A = \displaystyle \large{A\, =\, }∑k=1N λk Vk VkT\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda_k\, V_k\, V_k^T}

. . . . .B = \displaystyle \large{B\, =\, }∑k=1N λk′ Uk UkT\displaystyle \large{\displaystyle \sum_{k = 1}^N\, \lambda^{'}_k\, U_k\, U_k^T}

. . . . .C = A B−1\displaystyle \large{C\, =\, A\, B^{-1}}
Click to expand...
You are given B as a series.

How would you express B-1 as a series?
 
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