Eigenvalues & Powers of Matrices

[@youngidealist]

Thank you for this. This is exactly what I was stuck on and found that I only needed to search for how eigenvectors can be applied to find your video.

[@shivanshgupta7492]

ture

[@shivanshgupta7492]

Very impressive vid
loved the concept and way u xplained

[@lil7725]

Thank you so much, this was very clear and understandable :)

[@ziadmathematics]

Thank you, amazing skills

[@chandjaved1108]

Very nice brother, good concept

[@polobobeetricethe3rd567]

hi is there a method for this where lamda is complex or either where there is only one value of lamda(where the quadratic is a perfect square)

[@slcmathpc]

It works just the same if the eigenvalues are complex numbers. As for your second question, the answer is it depends whether or not the geometric multiplicity matches the algebraic multiplicity; this is slightly more technical so I cannot really explain it in a comment, but suffice to say that not all square matrices can be diagonalized.

[@esissthlm]

Thank you! Interesting.

[@mechintosh]

Perfect!

[@segoviapatricio]

Hi, minute 09:24, why did you write the vector (1 -1) and not -1, 1 ??

[@slcmathpc]

papi chulo Any nonzero multiple of an eigenvector is also an eigenvector for the same eigenvalue; notice that one vector is the negative of the other.

[@segoviapatricio]

thanks for the explanation!!! good video.

[@slcmathpc]

slcmath@pc If A^n=PD^nP^-1, invert both sides to see that A^-n=PD^-nP^-1. Since D is a diagonal matrix, D^-n is obtained by inverting the individual eigenvalues along the main diagonal. This is of course based on the assumption that A is invertible and diagonalizable.

[@Jusexle]

thank you so much my exam is after 2 days

[@daixtr]

i noticed that instead of the usual det(A-lambda*I) you are instead using det(lambda*I - A) which resulted to elements of the matrix having reverse signs. Please clarify...

[@slcmathpc]

Dexter Aparicio This way, the characteristic polynomial is always monic even for a square matrix of odd dimension.

[@abrehambekele9620]

❤

[@LearnSpecialEnglish]

Thank you

[@segoviapatricio]

and for n

[@slcmathpc]

papi chulo If A^n=PD^nP^-1, invert both sides to see that A^-n=PD^-nP^-1. Since D is a diagonal matrix, D^-n is obtained by inverting the individual eigenvalues along the main diagonal. This is of course based on the assumption that A is invertible and diagonalizable.

[@lionking2424]

wonderful

[@andrewsantopietro3526]

I hope this works for fractional powers x,o

[@slcmathpc]

Have you figured it out? ;-)

[@aymadummeech]

Hello BSCS2C
Aral well :)

[@richard_darwin]

massive brain moment

[@slcmathpc]

Those are good. :-)

[@Mr.Coconut007]

PxDXPinverse=D

[@eletricman1998]

Ok so in this video