MHB What is the annihilator of a tensor in vector space V?

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Hi everyone, :)

This is a question I don't understand at all. What is the annihilator in this context? Hope you can help me out with this.

Problem: Find the annihilator of the tensor \(e_1\wedge e_2+e_3\wedge e_4\) in \(V=\left<e_1,\,e_2,\,e_3,\,e_4\right>\).
 
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Sudharaka said:
Hi everyone, :)

This is a question I don't understand at all. What is the annihilator in this context? Hope you can help me out with this.

Problem: Find the annihilator of the tensor \(e_1\wedge e_2+e_3\wedge e_4\) in \(V=\left<e_1,\,e_2,\,e_3,\,e_4\right>\).

Hi everyone, :)

I have received an answer to this question on Stack Exchange. I am trying to understand it but due to my limited knowledge of tensor algebra it will take a long time. :p

linear algebra - Annihilator of a Tensor - Mathematics Stack Exchange
 
The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...

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