M Theory Lesson 302
Assuming now that all matrix entries and scalars are complex numbers, let us consider a mass circulant $M$ in the form 
for two parameters $r$ and $\theta$. Under the nonassociative exponential product, $M$ acts on the right of the democratic matrix as a scaling, as in 
whereas its left action is of the form 
So when $\lambda = r = 1$, the special scale free value of $\theta$ results in a familiar choice for $M$, namely 
where $\omega$ is a sixth root of unity. Note that a zero element in a left hand factor results in a totally zero matrix, so the nonassociative product has many zero divisors.
for two parameters $r$ and $\theta$. Under the nonassociative exponential product, $M$ acts on the right of the democratic matrix as a scaling, as in 
whereas its left action is of the form 
So when $\lambda = r = 1$, the special scale free value of $\theta$ results in a familiar choice for $M$, namely 
where $\omega$ is a sixth root of unity. Note that a zero element in a left hand factor results in a totally zero matrix, so the nonassociative product has many zero divisors.
posted by Kea | 3:55 PM
1 Comments:
Grezt to see you blogging again! The M-theory posts are very informative and could someday form the basis for a book.
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