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Rational Canonical Form | My thoughts/summaries
https://mathwanderer.wordpress.com/2009/07/28/rational-canonical-form
Just another WordPress.com weblog. July 28, 2009. This post proves the existence of rational canonical form, using the structure theoerm of finite modules over PID. Another common canonical form is the rational canonical form. While Jordan form is more like a substitute for non-diagonalizable matrix and thus does not exist when the eigenvalues do not lie in the ground field, the rational canonical form exploits the properties of the characteristic/minimal polynomial. Matrix with coefficients in a field.
About | My thoughts/summaries
https://mathwanderer.wordpress.com/about
Just another WordPress.com weblog. I have been interested in math for a long time but I almost gave it up in the last two years. So this is a place for me to get myself back in and revise things I have learnt before. That said, the blogposts are intended to make my mind clear instead of being expository. Topics I would try to blog about/learn about recently:. Linear algebra: Kronecker product, Cholesky, SVD. AG: essentially Hartshorne chapter 1 and 2. I think I still have many things left ununderstood.
Smith Normal Form | My thoughts/summaries
https://mathwanderer.wordpress.com/2009/07/28/smith-normal-form
Just another WordPress.com weblog. July 28, 2009. This post proves the existence of Smith normal form. The proof is pretty much the same as the one of reduced row echelon form. Smith normal form is a generalization of Gaussian elimination to matrices with coefficients coming from PID. This can be used, for example, in finding a. Theorem 1 (Existence of Smith Normal form). Matrix with entries in a PID. Both invertible, such that. Is of the form. The proof is similar to the Gaussian elimination process.
August | 2009 | My thoughts/summaries
https://mathwanderer.wordpress.com/2009/08
Just another WordPress.com weblog. Archive for August, 2009. August 22, 2009. Varieties II: Quasiprojective Varieties. August 17, 2009. Varieties I: affine varieties. August 2, 2009. Similarity and normal forms. Soarerz on Smith Normal Form. Messi on Smith Normal Form. On Jordan form II: Computati…. Soarerz on Smith Normal Form. Ptp on Smith Normal Form. Blog at WordPress.com. Create a free website or blog at WordPress.com. Follow “My thoughts/summaries”. Get every new post delivered to your Inbox.
Similarity and normal forms | My thoughts/summaries
https://mathwanderer.wordpress.com/2009/08/02/similarity-and-normal-forms
Just another WordPress.com weblog. Similarity and normal forms. August 2, 2009. This post will prove the uniqueness of Jordan form, Smith normal form and Rational canonical form in an equivalence class of similar matrices. A criterion to check similarlity of matrices using these forms is given, and a nice lemma of similarity being irrelevant to field extension is shown using rational canonical form. Matrix (over an algebraically closed field. We have seen in a previous post. Once we have put the matrix.
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My thoughts/summaries | Just another WordPress.com weblog
Just another WordPress.com weblog. Varieties II: Quasiprojective Varieties. August 22, 2009. This post contains the definition of (quasi-) projective varieties, regular functions, morphisms, projective coordinate ring, the Nullstellensatz. It also contains the global section of sheaf of regular function over distinguished open sets and the fact that affine neighborhoods form a basis for the Zariski topology. From → Algebraic Geometry. Varieties I: affine varieties. August 17, 2009. August 2, 2009. This p...
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