Example of Jordan Canonical Form: Real 4x4 Matrix with Basis 2

Matrix Theory: Find a matrix P that puts the following real 4x4 matrix A = [2 0 0 0 \ 0 2 0 0 \ 0 0 2 1 \ 1 0 0 2] into Jordan Canonical Form. Here the JCF has blocks of size 3 and 1. We focus on finding a vector that generates the 3x3 block.

[Christian-qhzu]

I cannot thank you enough for this video. I was so confused about how to put a matrix into Jordan form, and you made it super clear. You're an excellent teacher!

[cmdstraker]

Is there a video where you talk about the method for determining the block sizes in a bit more detail?

[INDIANANA]

thanks. mathdoctorbob for these wonderful videos...

I have one question.

when the vectors v and w are listed between 1:25 and 1:32, shouldn't the vector v be like [0 0 0 1] ?

the video shows that
v=[ 0 1 0 0] and w= [ 0 0 1 0] generate the null space. I find it incorrect. Can you throw some light on this doubt ?

[mattia]

Why does at 5:20 [1, 0, 0, 0] correspond to v3 ?

[xaifax]

im having trouble finding the eigenspace for [1 0 0 2/3 / 0 1 2 -1/3 / 0 0 0 0 / 0 0 0 0] any help there?

[thatsmothereffinscience]

I am curious as to why you chose to take out the components that you did (set to zero). I understand why we took ..say 'x' number to zero, but what aided in your choosing of those specific ones?