# Questions tagged [determinant]

Questions about determinants: their computation or their theory. If $E$ is a vector space of dimension $d$, then we can compute the determinant of a $d$-uple $(v_1,\ldots,v_d)$ with respect to a basis.

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### Verification of a demonstration

I need to know if the proof I made for the following problem is correct. Problem: If C is a matrix of order $3 \times 3$ such that $\text{rank}(C) = 2$, then $\text{det}(C) = 0$ Proof: If it must be ...
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### Jacobian of the vector reflection operator

While re-deriving some equations relevant to Monte-Carlo path tracing (specifically, the probability distribution of sampling a specific light direction from Sampling the GGX Distribution of Visible ...
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### Does there exist a square matrix $B\neq O$ of order $n>1$, such that for every square matrix of order $n$ we have $\det(A+B)=\det(A)+\det(B)$?

This is a follow up to my previous question. There it was shown that for every square matrix $A$ of order $n$ there exists a square matrix $B\neq O$ of order $n$ with $\det(A+B)=\det(A)+\det(B)$. The ...
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### Intuition for Laplace expansion

I've been trying to look for an intuitive understanding for the Laplace expansion of the determinant. I first tried looking for the proof but let's just say it was way to complicated for my ...
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