Proving matrix equations. (English) Zbl 1050.15015

Deutch, Michael

Southwest J. Pure Appl. Math. 2004, No. 1, 54-56 (2004).

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 \(A_{\lambda }\), \(A_{\mu }\).

Reviewer: Vladimir P. Kostov (Nice)

MSC:

15A24

Matrix equations and identities

Keywords:

symbolic matrix equation; (in)dependent variable; primitive number; normal form