# Tagged Questions

Question about determinants, computation or 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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### Determine the eigenvalue of a real matrix

I think to this question for two days : Let $A$ be a $3\times3$ real matrix such that $\det(A) = 1$ and $A^{-1}= A^T$. Prove that one of the eigenvalues is equal to $1$. I used the fact that ...
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### A determinant associated to point sets in the plane

Consider $n$ distinct points in the plane $z_1, \ldots, z_n$. Form the matrix $D$ containing their squared distances as entries: $$D_{ij} \ = \ |z_i - z_j|^2 \, .$$ Obviously, this matrix is ...
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### evaluation of determinant without expanding

If $\;\det \begin{pmatrix} a & x & x & x \\ x & b & x & x \\ x & x & c & x \\ x & x & x & d \end{pmatrix} =f(x)-xf’(x)$ where $f'(x)$ denotes ...
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### What is the determinant of exp(matrix)? [duplicate]

Given a square matrix $A$, form the Lie series of it, which is defined by: $$e^A = I + A + \frac{1}{2} A^2 + \frac{1}{3!} A^3 + \cdots + \frac{1}{n!} A^n = \sum_{k=0}^\infty \frac{1}{k!} A^k$$ Is ...
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### What is the meaning of cofactor expansion?

I understand how to perform a cofactor expansion in finding the determinant. Can you explain what this method is really capturing or what thinking leads us to use this method?
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### Finding the determinant of a $4 \times 4$ matrix

I'm trying to find the determinant of this $4 \times 4$ matrix $$\begin{bmatrix}3&0&0&-2\\-3&0&-3&0\\0&3&0&-2\\0&-2&2&0\end{bmatrix}$$ I'm also trying ...