Example of Gram-Schmidt Orthogonalization

Linear Algebra: Construct an orthonormal basis of R^3 by applying the Gram-Schmidt orthogonalization process to (1, 1, 1), (1, 0, 1), and (1, 1, 0). In addition, we show how the Gram-Schmidt equations allow one to factor an invertible matrix into an orthogonal matrix times an upper triangular matrix.

Category:

Education

Tags:

• Mathematics
• linear
• algebra
• Gram
• Schmidt
• orthogonalization
• basis
• orthonormal
• invertible
• matrix
• triangular
• orthogonal
• decomposition

[Dominic83189]

you are the strongest math doctor ive ever seen

[MathDoctorBob]

@Dominic83189 I break chalk like it is no one else's business. It's actually kind of annoying. :) - Bob

[yotube123454321]

First midterm tomorrow. I've just been memorizing the orthogonalization formula this whole time. I actually understand where it came from now. Thanks a lot. Keep making videos! There are so few **good** higher-level-math videos on the web.

[MathDoctorBob]

@yotube123454321 You're welcome! Good luck with your exam.  Please let me know if you a looking for specific problems. - Bob

[MathDoctorBob]

@arghya995 You're welcome!

[arghya995]

grt lectr.......... thankzzz a lot:-)

[candamohcine]

You're Great Professor :)

[Silvyanutza]

Hi!Could you put down the matlab code for this if you don't mind!I'd really apreciate it!

I'd like to see how can i compute a QR FACTORIZATION in MATLAB ,my explained steps!Thanks a lot in advance!I'm student at Polytehnic University of Bucharest and i need it so much!!

[MathDoctorBob]

@JQ322 You're welcome, and thanks for the comment. I can definitely do that. Are there any specific problems that you want to see? - Bob

[JQ322]

Could you post up a video on QR factorization. I guess its too late for me, but might be helpful for others, as there arent a lot of video's such as yours for it. Thanks!