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I want to understand how one can find the exterior product of square matrices. I searched about it and I find a lot of complicated formulas and without any examples. On the other hand, I found this anwser that contains a nice example. What I understood from the example is the new matrix ( I meant the exterior product one) comes from the determinant of minors of the original matrices. I want to know whether we have a similar thing for the higher-dimensional case.

Let me ask my questions better, 1) Does one can calculate the exterior product of square matrices by calculating minors of the original one? 2)Let $A$ be a $5 \times 5$ matrix. Can one give a concrete example that calculates $\wedge^3 A$? Thanks in advance

Adam
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  • The answer to (1) is yes. On this post, I provide a proof of the formula for the entries of the matrix associated with $\wedge^2 A$, but this proof can be extended to higher exterior powers as well. – Ben Grossmann Apr 17 '21 at 20:38
  • Regarding (2): you're asking us to compute a $10 \times 10$ matrix. Is there another approach we could take here? Would you be satisfied with a python script that computes this matrix? – Ben Grossmann Apr 17 '21 at 20:42
  • @BenGrossmann : Thank you very much for your comments. Yes, A python script is great. – Adam Apr 18 '21 at 16:06
  • @BenGrossmann I would really appreciate it if you could email it to me; adamrt88@gmail.com – Adam Apr 18 '21 at 16:13

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