Hm... I think I will do a little visual intuition #LiaScript doc about the determinant and how it corresponds to area/volume 🤔 I feel that many people are very confused by the #determinant when they encounter it in a linear algebra #math class. At least in mine, it was this weird abstract function (granted, this way of going about things also has its positives), not like a geometric thing. Then you see it popping up in like multivariate integrals with volume elements and its like... huh?

I'm reading Artin's #GaloisTheory and I'm wondering if the #math exposition of the #matrix #determinant relying on homogeneity properties is related to the #BrunnMinkowski #inequality

I will check my handwritten notes when I'll be in Poland end of July but I remember that homogeneity played a role there.

This rambling is related to my struggle to understand the #BrascampLieb and #rearrangementInequality. Any hints much appreciated 🥹😅🙈😊

Let me repeat that again!

That denominator of this fraction is the "DETERMINANT" that *determines* if we might have a problem when solving our system.

Therefore, it is a #determinant of that system.

Screenshot Saturday Mondays: dual-wielding katanas and duel-wielding fruit - https://www.rockpapershotgun.com/screenshot-saturday-mondays-swish-movement-and-marble-runs #ScreenshotSaturdayMondays #ScreenshotSaturday #SilentSanticado #WhimsicalHeroes #Indiescovery #Withersworn #Determinant #RetroSpace #MortalSin #AmidEvil #Enchain #Indie

In the Laplace or cofactor expansion of the determinant of an \(n\times n\) matrix, the number of operations:
\[\text{Addition: }\mathcal{A}(n)=n!-1\]
\[\text{Multiplication: }\displaystyle\mathcal{M}(n)=n!\sum_{k=1}^{n-1}\dfrac{1}{k!}=\lfloor(e-1)\cdot n!\rfloor-1\]
\[\text{Both combined: }\displaystyle\mathcal{T}(n)=n!\sum_{k=0}^{n-1}\dfrac{1}{k!}-1=\lfloor e\cdot n!\rfloor-2\]
#LaplaceExpansion #Determinant #LinearAlgebra #Cofactors #CofactorExpansion #Matrix #Operations #Algorithm #Minors

#NS2 is a key #determinant of compatibility in #reassortant #avian #influenza virus with heterologous #H7N9-derived NS segment, https://doi.org/10.1016/j.virusres.2022.199028