# Tagged Questions

Questions about the determinant of square matrices or linear endomorphisms. Also for closely related topics such as minors or regularized determinants.

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### What's the maximum determinant of the (0, 1) matrix from M(n, R)?

If there's no exact formula what's the nearest upper and lower bounds do you know?
The determinant behaves multiplicatively with respect to the usual matrix product $$\det(AB) = \det(A)\det(B),$$ and also with respect to the Kronecker (or tensor) product of square matrices $$\... 0answers 941 views ### Determinant of a sum of a diagonal matrix, a dyadic product matrix, and a Hermitian Toeplitz matrix Hi From a physics problem, I am trying to evaluate exactly the following kind of determinant: G = A + M + N. A is diagonal M is a product of a column (of 1s) and a row matrix N is a Hermitian ... 1answer 818 views ### Appropriate journal to publish a determinantal inequality I have recently made the following observation: Let v_i := (v_{i1}, v_{i2}), 1 \leq i \leq k, be non-zero positive elements of \mathbb{Q}^2 such that no two of them are proportional. Let M... 2answers 3k views ### Determinant of a 3x3 Magic Square Hello guys. This is my first question with mathOverflow so I hope my etiquette is up to par here. My question is regarding a 3x3 magic square constructed using the la Loubere method (see la Loubere ... 19answers 23k views ### Why were matrix determinants once such a big deal? I have been told that the study of matrix determinants once comprised the bulk of linear algebra. Today, few textbooks spend more than a few pages to define it and use it to compute a matrix inverse. ... 6answers 3k views ### Expressing adj(A) as a polynomial in A? Suppose A\in R^{n\times n}, where R is a commutative ring. Let p_i \in R be the coefficients of the characteristic polynomial of A: \mathop{\mathrm{det}}(A-xI) = p_0 + p_1x + \dots + p_n x^n.... 0answers 255 views ### Function recursion relation over symmetric group Hi! Let P be a permutation in the symmetric group SN and let π=πj, j+1 be a transposition of elements j and j+1 of the permutation. Let A(P) be a function in dependence of the permutation P. P&... 1answer 542 views ### Hankel determinants of symmetric functions The starting point is that it is known that the Hankel determinants for the Catalan sequence give the number of nested sequences of Dyck paths. I would like to promote this to symmetric functions. ... 3answers 2k views ### Splitting the determinant polynomial into linear factors - a Dedekind problem Here's the question in a nutshell. For some n\in\mathbb N, we consider the polynomial \det\left(\left(X_{i,j}\right) _ {1\leq i\leq n,\ 1\leq j\leq n}\right)\in\mathbb Z\left[X_{i,j}\mid 1\leq i\... 2answers 1k views ### What are picard categories, where can I learn more about them, and why should I care to? I have the category-theoretic background of the occasional stroll through Mac Lane's text, so excuse my ignorance in this regard. I was trying to learn all that I could on the subject of tensor ... 3answers 2k views ### Sarrus determinant rule: references, extensions SEEKING REFERENCES FOR SARRUS' RULE AND EXTENSIONS An undergraduate came to me with an identity for 4x4 determinants that is actually correct: \det(A)=h(A)+h(RA)+h(R^{2}A) where R cyclically ... 2answers 1k views ### Lifting matrices mod 2 to integers. The following question was motivated by my research. Consider a n\times n matrix whose elements are 0's or 1's such that the determinant is odd. The question is: is it possible to assign signs ... 2answers 2k views ### Statement of Lagrange's theorem on determinants(elementary question). Apologies for this elementary question; but I was unable to find a reference otherwise. Let A, B, C be square matrices of the same dimension. Then,$$\begin{vmatrix} A & C \\\ 0 & B \end{...
By a pairing on a vector space $V$, I mean a linear map $A : V \otimes V \to R$. If $V$ is $n$-dimensional ($n < \infty$), then I can define the determinant of $A$ by considering the canonical ...