Linear Algebra - Change of Variables in a Quadratic Form

[@Olivia-tl1le]

i have an exam tomorrow - thank you sir!!

[@chinny872]

This was really helpful. Thank you!

[@arnoldyim4765]

I'm glad that it was helpful!

[@sidharthsubbarao1923]

saving my career

[@godcaresndubuisi4190]

, You're so good sir. Well understood

[@souvikdolai609]

Great explanation . Sir please make video on bilinear form.

[@dilaygunay1432]

Thank you for making this video.

[@shivamkak7981]

Very well-made video

[@dougwalker6835]

Great and very helpful. THANKS.

[@guttensomforsvant]

In your example, what happens if A is 3x3? with 3 different lambda values? How do I go about changing variables then?

[@arnoldyim4765]

If A is 3x3 and you have 3 eigenvalues, you'll want to find an unit eigenvector for each eigenvalue. Then you can make a matrix P with those unit eigenvectors as columns (if you have 3 distinct eigenvalues you this matrix P will have orthonormal columns). Your change of variables would still be x=Py, or y=P^Tx. You might check out these videos for more on orthogonal diagonalization of symmetric matrices (I go through examples of diagonalizing 3x3 matrix): kzbin.info/www/bejne/lZubp32YeL5mhNE kzbin.info/www/bejne/gIqUi6BudrlleMU

[@keerthymahesh1382]

Sir how is root 5 is obtained

[@JacobLuHK]

length

[@notmymemes4209]

thank you

[@richardpatove4587]

thanks

[@mr.cutter5001]

i think its not root 5. its just 5 (2^2+3^2)^1\2=5

[@danhn4658]

anh em thầy Thịnh giơ tay

[@shIong]

nice