Wednesday, 1 July 2015

linear algebra - Proof about diagonal matrices

Suppose that AMn×n(R) such that their eigenvalues are {λ1,,λn}, i.e. σ(A)={λ1,,λn}, then if the geometric multiplicity mgA(λi) is the same arithmetic multiplicity maA(λ), we have that A can be diagonal

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real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...