Householder Transformation with QR Decomposition Examples.

Householder Reflection or Transformation is one the methods of decomposing a matrix into an Orthogonal Matrix (Q) and Right Upper Triangular Matrix (R). It helps to solve systems of equation using backward substitution.

[jcfer]

Just wanted to say your whole channel, numerical methods + examples, is absolutely solid! Thank you so much for the hard work!

[AidanHomewood]

Bro you are incredible. Best explanation I've heard after ages of trying to understand how to do this. Keep it up man.

[rjk.]

Super helpful, first clear and concise video explaining it I found. Thank you !!

[veenanarayanan]

Thank you for the explanation sir. In the first example, the signs of all the elements in the second column of Q2 is positive. The first entry of the third column of Q2 is positive and the sign of third entry is negative. i.e Q2= H1*H2=[ -0.5774 0.4083 0.7071; 0.5774 0.8165 -0.0000; -0.5774 0.4082 -0.7071]. Therefore, Q2*R2=B.

[planetariansaturn]

This is amazing help with linear algebra, I thank you so much helped a lot

[ioannisvarnas]

Such an amazing explanation
Good Job !!!

[ae]

Thanks man. in the book it was not clear to me. you helped me a lot. thanks.

[mbc.]

Great explanation, thank you very much!!

[georgeklimov]

Thank you for the video, I learned a lot. I would like to point out that there is a mistake on the second problem, I will not explain it here but Q = P1P2 has a calculation error. Otherwise, phenomenal video!

[HKHasty]

Very helpful, how come though you aren't taking the sign of first element in x to calculate v?
v_k = x+sign(x_k) ||x||_2 e_k, with k being column number on original matrix B.

[MrNike]

you should mention that u1 = a1 + sign(a_11)||a1||e1. It's not always minus.

[MoumitaMandal-dp]

Q2= (H2 H1)^ T, Transpose is missing. Though here both are same

[founderinho]

What should we do with complex matrices?

[ryanjacksonx]

Doesn't x1 itself usually come from a matrix? Can you show or explain that?

[bhageshmaheshwari]

In the two examples sign of first element was different but you still used - ? Is that a mistake ?

[ricardoraymond]

Nathan kutz covered the same topic, and only he and god knows what he is talking about.