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- #1

- Feb 5, 2012

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Here's a question I am trying to solve at the moment. I want to know what is meant by decomposable in this context. Really appreciate any input.

**Problem:**

Let \(V\) be a vector space over a field \(F\), \(\{e_1,\,e_2,\,\cdots,\,e_n\}\) a basis in \(V\) and \(\{e^1,\,\cdots,\,e^n\}\) adjoint basis in \(V^*\). Which of the following tensors, given by their coordinates are decomposable:

a) \[t^k_{ij}=2^{i+j+k^2}\]

b) \[t^{ij}=i+j\]