The Jordan Form of a 3 by 3 matrix: Example 1

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We give an example of finding the Jordan form of a 3x3 matrix. The algebraic multiplicity of the only eigenvalue is 3 and the geometric multiplicity is 1. The Jordan form has two ones above the main diagonal.

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Finally. Your method is the easiest I saw. Most examples just use a huge system of equations to try and find each term of the matrix in Jordan form, but yours is way more simple! Thanks!

TheJoaovicente

Sorry professor I don’t quite get in 9:59. How can you immediately get the Jordan matrix {{9, 1, 0}, {0, 9, 1}, {0, 0, 9}}? I know that the diagonals should be 9 because 9 is the eigenvalue, but how can you determine the 1s and 0s in the other entries of the matrix? Can you teach me please? Thank you🙏🙏🙏

sultanhsu

Thank you prof Mike, your analysis and linear algebra lectures are wonderful

tianshugu

Hi, many thanks, you made something click for me! Say, is it standard to teach the entire proof of computing a Jordan form? It's very pretty and interesting to grasp, but given the practical uses, it seems so redundant.

hhhhheeeelllllllllooooo

you sound alot like MatPat! thank you for the video.

yassinenajar

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