Example of Rational Canonical Form 1: Single Block

Matrix Theory: Let A be the real matrix [0 -1 1 0 \ 1 0 0 1 \ 0 0 0 -1 \ 0 0 1 0]. Find a matrix P that puts A into rational canonical form over the real numbers. We compare RCF with Jordan canonical form and review companion matrices. (Minor corrections added.)

[kevinmartins]

thank you very much. I'm a brazilian student of mathematics and you saved my final exams on Linear Algebra 2

[MathDoctorBob]

RCF is a weird topic. It doesn't appear in as many applications as Jordan form, and it is often cut completely if no time. My professors were acutely aware of this, so I had to learn it in at least three classes. - Bob

[zhouryan]

Thank you very much! Can you explain why # blocks = dim ker q(A) /deg q(x)? (3:05)

[MathDoctorBob]

@candamohcine It's the same video from a few days ago. I reshot a few boards to fix some items, probably at a slower pace. - Bob

[timsetsfire]

Wonderful video. Your instruction is excellent. I am sure I will watch this several more times. Thank you!

[MathDoctorBob]

@timsetsfire You're welcome! I really enjoy this material. - Bob

[ericreeves]

My god this is so helpful you saved my finals thank you very much

[notSoFormal]

Why are there so few views? Do most lin alg classes skip this?

[hcostareis]

Hey Bob! The matrix A^2+I has two wrong entries. It is -2 instead of -1 and 2 instead of 1. Great video though.

[MathDoctorBob]

You're welcome, and good luck on finals!

[MathDoctorBob]

Thanks! Good eyes. The typos always find a way.