Linear Algebra 5.2.2 The Characteristic Equation

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Kimberly Brehm

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THANK YOU SO MUCH I THOUGHT MY TEACHER WAS JUST LOOKING AT A MATRIX AND MAKING UP NUMBERS!!! NOW I KNOW!!!

crabcakeenthusiast

شكرا شكرا
you make things easy, enjoyable THANK YOU from Egypt

AhMedKhaled-omly

on the practice, did you mean to write lamda^3 for the last term? In the problem is was to the first power.

matt

Hi, can you please make a video for section 5.3 and 5.4? Thank you!

marthabarranco

But the equation isn’t lambda ^ 3, it’s just lambda. was there a typo in the question maybe ?

ozlempolat

You did not write out the last polynomial (in pink) correctly, you left out the ^3 on the 3(lambda).

grapplegamer

you're a life saver thanks so much for linear algebra video

bisrataraya

Ok so we can only find characteristic equation for square matrix only?

debjitkhaskel

5:57 how did you calculate it so quickly

muhammadabdullahriazbhatti

But what about the complicated ones? There are more concepts right??

saminyasar

Can you add the sections in-between 5.2 and 6.1 please 🙏

pringlegodx

Characteristic equation can be calculated without determinant
We can use trace and multiplication
a_{n}=1
a_{k} = -1/(n-k)sum(a_{j+k} tr(A^{j}), j=1..n-k)
This can be proved using fact that tr(A^{m})=sum(λ_{k}^{m}, k=1..n)
after this we will get sum of powers which is symmetric function so Newton-Girard formulas will be helpful
Vieta formula also will be useful to express elementary symmetric polynomials in terms of coefficients
The other method is using Cayley-Hamilton theorem
We pick randomly chosen vector and plug in matrix into characteristic equation
this will lead us to the system of equations for coefficients

holyshit

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