## Proving matrix equations.(English)Zbl 1050.15015

The author presents a method for determining the truth of symbolic matrix equations where $$0$$ or more such equations are given as true. One writes the equation to be proved in terms of independent variables only removing the dependent ones. Example: given $$A_{\lambda }=(\lambda -A)^{-1}$$ and $$A_{\mu }=(\mu -A)^{-1}$$, prove that $$(\lambda -\mu )A_{\lambda }A_{\mu }=A_{\mu }-A_{\lambda }$$. Here $$\lambda ,\mu \in {\mathbb C}$$ and the $$n\times n$$-matrices $$A$$, $$A_{\lambda }$$, $$A_{\mu }$$ are invertible. The independent variables are $$\lambda ,\mu , A$$, the dependent ones are $$A_{\lambda }$$, $$A_{\mu }$$.

### MSC:

 15A24 Matrix equations and identities
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