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WEBJul 18, 2017 · Trivial seems to be more background relative and subjective, while degenerate is more intrinsic, degenerating some structure. So all four combinations are possible: trivial and degenerate (0 matrix), non-degenerate but trivial (identity matrix), …
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See results only from math.stackexchange.comWhat defines "triviality"?
1) Trivial sub-objects, i.e. if $G$ is a group, then $1, G \leq G$ are trivial subgroups …
inequality
From what I understand, a degenerate triangle is a triangle that has collapsed …
WEBDegenerate cases are cases that are special, require special handling because the usual assumptions fail, and simplify the situation in certain way. For example, if you have 3 …
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WEBMar 7, 2019 · A "trivial case" is a case which a simple, limited algorithm could still solve. For instance, the case where you need to sort a list of numbers, but they're already …
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In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class; "degeneracy" is the condition of being a degenerate case.
The definitions of many classes of composite or structured objects often implicitly include inequalities. For example, the angles and the side lengths of a triangle are supposed to be positiv…Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 6 mins
WEBIn every case with B2 4AC, the roots are real. The solutions y.t/ have growing exponentials or decaying exponentials. We don’t see sines and cosines and oscillation. The first …
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WEB1) Trivial sub-objects, i.e. if $G$ is a group, then $1, G \leq G$ are trivial subgroups of $G$. 2) Trivial solutions to a problem, i.e. $y=y'$ has a trivial solutions as a differential …
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WEBLeft: a stable degenerate node (in the case of only one linearly independent eigenvector). Right: an unstable degenerate node (in the case of two linearly independent …
WEB3 days ago · A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the …
WEBFeb 18, 2022 · We’ll start here with common instances of the phenomenon, in conic sections, pursuing the elusive case of a pair of parallel lines. Next time we’ll look at how …
WEBFrom now on, we only consider non-degenerate (V;q). To orient ourselves, it is useful to record the main properties we shall prove for the \good" groups associated to such (V;q): …
philosophy of mathematics - Are "A ∧ A" and "A ∨ A" degenerate ...
WEBNov 15, 2023 · Trivial seems to be more background relative and subjective, while degenerate is more intrinsic, degenerating some structure. So all four combinations are …
Understanding degenerate multivariate normal distribution
WEBMVN is degenerate when the covariance matrix Σ Σ is singular. I am trying to understand mainly conceptual (but also theoretical) implications of this. The Wikipedia article is quite …
Degeneration (algebraic geometry) - Wikipedia
WEBIn algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Precisely, given a morphism. of a variety (or a scheme) to a curve C …
inequality - Why invent the concept of degenerate triangle ...
WEBMar 19, 2023 · From what I understand, a degenerate triangle is a triangle that has collapsed into a line or point due to coinciding vertices or a side length of zero. But why …
Degenerate bilinear form - Wikipedia
WEBIn mathematics, specifically linear algebra, a degenerate bilinear form f (x, y ) on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V ) given by …
Time-Independant, Degenerate Perturbation Theory - A Study Guide
WEBMay 5, 2004 · We are now prepared to construct a new, complete, and orthogonal basis by joining the new set of states that we have specifically constructed to replace those states …
WEBSo the explanation is that, in some sense, these eigenvectors of the perturbed Hamiltonian is one of the possible choices of a basis of eigenvectors for the original space, and what …
What is the difference between singular matrices and degenerate …
WEBA matrix is degenerate if and only if the determinants of all its principal submatrices are non-zero (where the principal submatrices are the square matrices obtained by choosing …
What does "trivial" mean to you? : r/math - Reddit
WEBTrivial is when you think long enough, then you see that is true, with no computation. Obvious is when you don't need to think but you already know what step you should take …
Given three side of a triangle, how can I define whether it is a ...
WEBJun 26, 2018 · Given the side lengths a, b, c of the triangle, you can calculate the triangle's area via Heron's formula. If the area is 0 (or smaller than a given threshold, b/c of …
Degenerate distribution - Wikipedia
WEBIn mathematics, a degenerate distribution is, according to some, a probability distribution in a space with support only on a manifold of lower dimension, and according to others a …
schroedinger equation - Explicit nontrivial examples in quantum ...
WEBIt has a degenerate state in case of a symmetric potential, and the two associated states are non-degenerate when the potential is tilted (i.e. it becomes asymmetric). These …
logic - Are there Boolean homomorphisms from the degenerate …
WEBOct 2, 2017 · Take $\mathcal C=BA$, the category of Boolean algebras and homomorphisms between them. The terminal object is $\mathbb D$, the one-element …
Prevalence of asymptomatic valvular heart disease in the elderly ...
WEB2 days ago · The presence of trivial valvular regurgitation and that of aortic sclerosis were considered to be part of the normal spectrum and thus not included in the VHD group. ...
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