JEE Main & Advanced Mathematics Matrices Cayley-Hamilton Theorem

Cayley-Hamilton Theorem

Category : JEE Main & Advanced

Every matrix satisfies its characteristic equation e.g. let A be a square matrix then \[|A-xI|=0\]is the characteristics equation of A. If \[{{x}^{3}}-4{{x}^{2}}-5x-7=0\] is the characteristic equation for A, then \[{{A}^{3}}-4{{A}^{2}}+5A-7I=0\].

 

Roots of characteristic equation for A are called Eigen values of A or characteristic roots of A or latent roots of A.

 

If \[\lambda \] is characteristic root of A, then \[{{\lambda }^{-1}}\]is characteristic root of \[{{A}^{-1}}\].



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