# 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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### Area of a crossed diagonal quadrilateral

If four coordinates of vertices are given, the area of the first convex quadrilateral is expressed in known standard matrix form. How is the net (positive and negative sum ) area expressed for the ...
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### Determinant of circulant $(0,1)$ matrices of certain form

I am interested in computing the determinant of the following circulant matrices: let $n=p^k$ for $p$ a prime and $k\in \mathbb{N}$, take $a\in \mathbb{N}$ to be such that $a<p$ and $(a,p)=1$. ...
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### Does the Nullity Theorem hold in fields of characteristic 2?

I'm playing around with involutory ($M^2 = I$) matrices over finite fields with characteristic 2 ($\mathbb{F}_{2^m}$). I came across the nullity theorem, which seems very useful to check if ...
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### Rewrite proposition with logical symbols

I want to rewrite the following proposition in mathematical language (and by mathematical language I mean symbols such as: $\forall , \exists, (, ), \implies$ and so on). Proposition: Every non-...
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### Is this an incorrect application of Tutte's theorem of perfect matching for bipartite graphs?

This is an extract from a conference paper. It seems the authors are invoking Tutte's theorem (since  refers to the 1947 paper) to conclude that a matrix $J(x)$ with given numerical entries is ...
1 vote
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### Tutte's matrix for perfect matching in bipartite graphs

I came across Tutte's matrix for a bipartite graph $G(U, V, E)$ in two different forms. One form (seen in these notes for example https://www.cs.cmu.edu/afs/cs/academic/class/15859-f04/www/scribes/...
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### Determinant of a special diagonal matrix

I have a matrix of:  A = \begin{bmatrix} a & b & b & \cdots & b \cr -1 & 1 & 0 & \ddots & \vdots \cr 0 & -1 & 1 & \ddots & \vdots \cr \vdots & \...
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### Invertibility of the Gram matrix of convex combination

I am struggling with this this question: Let assume two real valued matrices $A,B\in R^{w\times d}$, which $w>d$ and they both have full (column) rank. Now, I am interested to study invertibility ...
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### Determining value of constants in simultaneous equations using inverse matrix when determinant is zero

I've been having trouble understanding how to solve this problem: Determine the values of the real constants a and b for which there are infinitely many solutions to the simultaneous equations 2x + 3y ...
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### Determinant inequality with unitary matrix

I come up with the following conjecture while doing my research, which is a determinant inequality. I have tried to run the MatLab simulation to verify its sanity. It seems that the inequality is true....