Math 202C: May 18 Lecture

*** Problems in this lecture due May 24 at 23:59 ***

Problem 18.1. A tensor t \in V \times V is said to be decomposable (or pure) if it can be written as t=v \otimes w for some v,w \in V, and indecomposable otherwise. Show that indecomposable tensors exist.

Problem 18.2. Given a Hilbert space V, establish the orthogonal direct sum decomposition V \otimes V = V \wedge V \oplus V \vee V. For V finite-dimensional, calculate the dimensions of all spaces involved in this decomposition.

Published by Jonathan Novak

Mathematician at UC San Diego.

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