Proof of - Geometric Multiplicity is less equal Algebraic Multiplicity

[@pcalde256]

Finally, great job man

[@DrMathaholic]

Thank you 😊

[@utkarshraj3272]

Very Good Video Sir🙏, I have a doubt how is the matrix an upper truangular matrix?

[@DrMathaholic]

Thank you . At 9:24, You are asking? We can write the matrix as a block matrix, while doing that, bottom left entry is 0. So when you look the matrix as block matrix it's upper triangular

[@sam-u8y9y]

Hi Sir, It is very interesting to see this proof. I have a query, How can we say g(x) may have lambda? If there are no chance of having lambda inside g(x), then proof is AM = GM right.

[@DrMathaholic]

Yes, correct...in that case AM=GM

[@KesharinanadanSoni]

Sir mera Ek question if lamda is eigen value of matrix A with charactristics polynomial f(x) (x_l) k /f(x) and x_l) /_f(x) then geomertical multipicity of lamda is most is at most k

[@DrMathaholic]

@user-xs2hy8vv1w if lambda is an eigenvalue with Algebraic multiplicity k then geometric multiplicity of lambda is almost k

[@KesharinanadanSoni]

Sir please solve

[@KesharinanadanSoni]

Sir i want talking you

[@KesharinanadanSoni]

@@DrMathaholic I don't understand that mean lambda is multiplicity is k is right

[@DrMathaholic]

@@KesharinanadanSoni that means lambda is appearing k times as a root in characteristic equation...

[@SNEHAJAISWAL-oc9xl]

Thanks sir

[@ruchimishra8775]

Thanks 🙏 sir

[@DrMathaholic]

Welcome 😊