Example of Spectral Decomposition

Linear Algebra: Let A be the real symmetric matrix [ 1 1 4 / 1 1 4 / 4 4 -2 ]. Using the Spectral Theorem, we write A in terms of eigenvalues and orthogonal projections onto eigenspaces. Then we use the orthogonal projections to compute bases for the eigenspaces.

[Iceiam]

GREAT WORK MAN! I cant wait until you get the recognition you deserve for your vast and extremely useful videos! Keep up the good work, it will/is making a big difference to Mathematicians everywhere. God Bless!

[TheAllotrope]

Fantastic job! I was really hurting, not understanding spectral decomposition one bit, and this video finally made it click. Thank you, sir.

[Folopolis]

This video filled in a key gap the Khan Academy left out, it really helped in my linear algebra class.

[karr]

I haven't been able to find the source like your lecture helping me to understand at all complex concepts so far as I'm patient. Thanks a lot

[yjsnpi]

thank you Bob. you saved my life as i just understood this (40 minutes before final exam)

[jonathan]

Thanks a lot Bob. I've been trying to learn some of the theory behind principal component analysis and this has helped a ton!

[parijatbhowmick]

Very Helpful for students.. Thanks for the video session..

[xinyuwang]

Thank you, Bob, after having followed your lectures, the spectual theory no more puzzles me. Well and clearly explained. :)

[MathDoctorBob]

@Iceiam Thanks for the support! I'm glad the channel is finding its audience. It's still a baby, and every new viewer is another incentive to do my best work. - Bob

[curtisw]

Why can't my prof teach like you thank you very much

[MathDoctorBob]

Thanks for the comment. Glad to be of help!

[MathDoctorBob]

You're welcome! I've actually use this one often in research.

[jinxinhe]

hey, doc Bob, thanks for your video a lot, that solves me a problem on finding projection operator, the book just confused me with the theorems and proofs with a choices of bad example, your video hits the points.

[洪偉哲-gl]

Thankyou so much. You helped me out of my final exam. I really do appreciate it^^

[singhsangha]

Very helpful and clearly explained, good video - Thank you!

[MathDoctorBob]

You're welcome, and thanks for the kind words!

[MathDoctorBob]

@TheAllotrope You're welcome! At heart, it's just diagonal matrices again with abstract nonsense. It turns out to be extremely important for physics. - Bob

[maximoiann]

Where did you found this projection formula on product? Is there any mathematical proof that's a projection formula, thanks.

[MathDoctorBob]

You're welcome! This was a fun one to shoot. - Bob

[aarthigummadi]

The same method can be used for determining matrix exponential?