Mathematics Stack Exchange
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Questions tagged [jordan-algebras]

This tag is for questions related to Jordan algebras. They constitute one of the first classes of non-associative algebras.

A Jordan algebra is a vector space endowed with a (generally speaking non-associative) product $(x,y)\mapsto xy$ that satisfies two identities:

  • [Commutative Identity] $xy=yx$ and
  • [Jordan Identity] $(xy)x^2=x(yx^2)$.

Jordan algebras were introduced by the physicist Pascual Jordan in 1932 as a new algebraic paradigm for quantum mechanics.

Since then they were studied extensively and found numerous applications. The interested reader is referred to a wonderful book "A Taste of Jordan Algebras" by Kevin McCrimmon.

35 questions
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Complex integration using a suitable contour

$$\int_{-\infty}^{\infty} \frac{x\sin x}{x^2 +4} \ dx$$ Can someone show me how to evaluate this integral by integrating around a suitable contour. I've seen similar questions however I think you have to use Jordan's lemma. Can someone show me…
erf44
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Proof of the formula for the number of Jordan blocks

here's what I need help with: Let A$\in M_{n\times n}(F)$ be a Jordanizable matrix. Let n$_k(\lambda)$ be the number of J$_k$($\lambda$) blocks. I'm trying to prove this formula: n$_k$($\lambda$)=rank($(A-\lambda)^{k+1}$)+rank($(A-\lambda)^{k-1}$)-2…
ToM446
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