Gram-Schmidt process example | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

Using Gram-Schmidt to find an orthonormal basis for a plane in R3

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[onebenp]

I've been going through the playlist of linear algebra and am really thankful for all the work that you have put in into creating the series. I am not able to attend any kind of formal courses due to Visa restrictions, but your videos are helping me to continue the pursuit of my education until I can go to university. Thank you again.

[domogami]

Wow, Here I am using this video from 11 and a half years ago to study for a Numerical Optimization midterm. I cannot thank Khan Academy enough

[Lortivar]

Linear Algebra final today! Here goes nothing...

[mathsvlog]

@ZaneMcCaig Gram Schmidt not only gives you a matrix in which every vector is a unit vector, but it also forms an orthogonal basis in which every vector is perpendicular to every other vector. Orthogonal matrices have some very useful properties (for example, orthogonal Q inverse = Q transpose; also, Q times Q transpose makes a projection matrix). This process may seem like a lot of work (and it is), but the result is very useful.

=Math

[willeett]

Can't we just get the formula and how to use it? 

[petah]

thank you, final in 8 hours, helped clarified things

[Phagocytosis]

Have you tried watching it at 2x speed?

[Javlini]

09:15 is wrong. The projection should include the u1 on the right.

[dossie]

How do you make an extra vector (u3 or v3) to this basis? Since there are three coordinates in the vector is it possible?

[sunitachettri]

The absolute value or distance of Y2 =root 6/2 .if I am wrong please correct .

[yonghuiliew]

Why do you assume x2 and x3 as free variables at the beginning of the video?

[mynameismegaloser]

I'm not really sure how using the f word relates with being in the university.

[sam]

Facts about khanacademy - dont hate me

[AlexanderAV]

@petah604 Shit finals in winter? Mine is tomorrow =D

[MannyFreshNovoa]

Sometimes you just need to get to the answer

[malekhakim]

the program of Gram Schmidt Process for a dimension d*n

[jxcxtxl]

I hate this Gram-Schmidt law thing... so confusing. and midterm is in 3 hours....

[sam]

@oneben

with this attitude, i doubt you`ll ever make it to university. ppl who use f words are normally not seen in next term classes. u my friend will not be seen anywhere close to unviersity.

once u fail acheive ur goal, u can always return to this screen and thank khansAcademy lol

[A-]

Beat that guys, my final is after 1 hour and 35 minutes

[MoreKevinLiang]

i've been watching your vids for a while now....but seriously, I cannot understand you. You need to be more coherent while you speak, instead of going back here and there.
Otherwise, I follow your work perfectly