3.3.2 Householder transform, part 3

Advanced Linear Algebra: Foundations to Frontiers
Robert van de Geijn and Maggie Myers
For more information: ulaff.net

[@EngSeifHabashy]

I love how simple, straight to the point, short his explanaition
Thank you sir!

[@realnameverified416]

Splendid! I wish I could like the video more than once!

[@oronimbus]

the geometric interpretations are very useful! thank you

[@Unknownfor13]

explain it very well!!!

[@engineeringoyster6243]

Thanks for the video.
After a 40 year career as a flight dynamics engineer at a major manufacturer of jetliners, I have under taken as a hobby to manually calculate the eigenvalues and eigenvectors of a flight dynamics problem. When I was working, I would just fire up MatLab and use eig.
One detail that has tripped me up as I've studyed this is that the folks in linear algebra who use the term "reflection" really mean "refraction." I say this because the vector doesn't reflect off of the plane but refracts thru the plane.

[@knufyeinundzwanzig2004]

is a refraction like this even possible? I think reflection makes more sense as it is referring to the mirror image

[@jakobjonsson1474]

This is very beautiful! Thank you for the clear and understandable explanation!
/Jakob Jonsson

[@Unknownfor13]

Thanks sir

[@yb801]

thanks, really helpful, now i now why we need to do qr decomposition this way, instead of just use the formula without knowing why.

[@filipzet4120]

thank You!

[@rav2n]

if one knows the 2.norm of x and the standard basis e, then beta e directly gives the required mirror vector along e right. Then why do we need to represent the "mirror" operation as a matrix in terms of u in the first place?