Eigenvalues and Stability: 2 by 2 Matrix, A

[@noah-732]

This video is the level of instructional video that all math videos on youtube should strive to achieve

[@farbodghanonui4482]

This is probably the best lecture anyone can be in . Thank you .

[@ksbalaji1287]

Gilbert Strang is The One. The master of the Matrix.

[@diegolainfiesta]

How smooth his explanations...crystal clear! Thanks!

[@georgesadler7830]

That you MIT for this mathematical giant. Dr. Strang you are the best.

[@59entoni]

At M.I.T. Prof. David Jarison and Prof. Arthur Mattuck are also outstanding.

[@Thijmen688]

10:44 quick mahfz

[@Kanidrum]

What beautiful explanation! Thanks, professor.

[@gopeshthakur1020]

Jump to 10:59 , stability !

[@rafaelsouza4575]

ok, now my mind blew when the laplace transformation met eigenvalues.

[@raniaelsebai9889]

Thanks Professor for your cooperation

[@eloymarquez4783]

This is gold. Thank you professor! Thank you MIT

[@caiozowyecamachocabral5413]

Thank you from Brazil.

[@jonathansum9084]

shouldn't the solution go to 0 if it passes the stabiility test? I am talking about the saying in the very last second.

[@hishamsaadeh1717]

yes it should, he said that by mistake

[@akshayramachandran7857]

Need not be, stability implies solution doesn't diverge off, anymptotic stability implies convergence to 0

[@rakhimovv]

Certainly power of the exponents (\lambda t) will go to minus infinity in case of stability, then the exponents will go to zero. I guess that's what the professor was thinking to say

[@davidflores881]

question! in a det ad-cb ^^^^ this shouldnt be zero or it should be zero if we have a solution? I thought a matrix has a solution if the det is not zero

[@matheuscarvalho8890]

If we have only one solution for Ax=b, the determinant of A must be different than zero. If the determinant of A is zero, there are infinites solutions for the linear system or there is no solution.

[@asmaaabkari5202]

thank you from morroco

[@caiozowyecamachocabral5413]

OMG amazing class!

[@سلمىالترهوني-ي1ق]

المزيد من التمارين على استقرار المعادلات التفاضلية والترجمة بالعربية

[@mgambowaghetohayupo1039]

thank you father of stability i exactly understand the concept

[@Zahidalizahidi]

very well sir---- from pakistan

[@hzlin6655]

Omg, fantastic explaination

[@ahmedismail1018]

to check the stability i have only to look trace and detremine

[@akshayramachandran7857]

Nope, it works only for above case (2nd order system)...for a general sense check stability by applying Routh Hurwitz criteria or by Lyaponav stability criterion

[@viccctv9106]

@@akshayramachandran7857 between the Routh Hurwitz and the Lyaponav which is better?

[@akshayramachandran7857]

@@viccctv9106 Lyaponav has a broader scope since it could be used for non-linear systems too.

[@charlottemackley8034]

I love this man!

[@engineershmily]

what for 3 x 3 and more matrix....?

[@Mohammad-fp7vu]

for 3*3 your eigenvalues have to be negative

[@carultch]

For 3x3 matrices, you need to solve a cubic formula to find the eigenvalues. Unless you are given special cases that can simplify with the rational root theorem and polynomial division.

[@Slime5276]

Thank you so much!

[@kaysenmortensen-chown9244]

thanks mister

[@araafdr]

nice

[@irfanjan1847]

KUCH SMAGH NHI AYA