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Trivial vs degenerate cases - Mathematics Stack Exchange
Jul 18, 2017 · Things are trivial when they are "like 1" and degenerate when they are "like 0". From another point of view, an object is trivial if you specifically exclude it from your proof, and degenerate if you specifically include it.
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Other content from math.stackexchange.comELI5 What are degenerate cases and trivial cases?
Degenerate cases may sometimes be easier [A, B, C on a line in that order], yet could also be harder [non-invertible matrices] or nonsensical [A = B when using angles]. So not all …
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Degeneracy (mathematics) - Wikipedia
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
Degenerate -- from Wolfram MathWorld
Oct 10, 2024 · A degenerate is a limiting case of a mathematical object that belongs to another, simpler class. For example, a point is a degenerate circle, and two identical roots are a …
What defines "triviality"? - Mathematics Stack Exchange
1) 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 equation, …
What is the difference between singular matrices and degenerate …
A 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 the same …
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Invertible Matrix - Theorems, Properties, Definition, …
An invertible matrix in linear algebra (also called non-singular or non-degenerate), is the n-by-n square matrix satisfying the requisite condition for the inverse of a matrix to exist, i.e., the product of the matrix, and its inverse is the identity matrix.
(ii) Φ is trivial, if and only if e= 0. Definition. Let Rbe a commutative ring with unit, and let Abe an R-algebra. Consider the product space A(1) = A×R, equipped with the direct sum R-module …
Is it acceptable to use the word "trivial" in lecture?
Jan 24, 2015 · Students may be offended or hurt if you call something "trivial" which they do not feel is trivial. Students may not view the word with the connotations you, or other posters on …
Understanding degenerate multivariate normal distribution
MVN is degenerate when the covariance matrix $\Sigma$ is singular. I am trying to understand mainly conceptual (but also theoretical) implications of this. The Wikipedia article is quite terse. …
Given three side of a triangle, how can I define whether it is a ...
Jun 26, 2018 · When you have three side lengths satisfying a ≤ b ≤ c and the sum a + b = c, then the triangle is degenerate. (Valid triangles have a + b > c and triangles with a + b < c are not …
Can a circle have radius 0? : r/learnmath - Reddit
A circle with zero radius is a degenerate or trivial circle, but it is still a circle. I have only ever seen a circle defined to be the set of all points x,y for which (x-a) 2+(y-b)2=r2
Degenerate Definition & Meaning - Merriam-Webster
The meaning of DEGENERATE is having declined or become less specialized (as in nature, character, structure, or function) from an ancestral or former state. How to use degenerate in a …
ON DEGENERATE NONMETRIC UNFOLDING SOLUTIONS. JAN DE LEEUW. Abstract. Loss functions proposed for nonmetric unfolding are discussed critically. Practical experience …
inequality - Why invent the concept of degenerate triangle ...
Mar 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 was it necessary to …
degenerate, v. meanings, etymology and more - Oxford English …
Learn the nine meanings of the verb degenerate, from anatomy to mathematics, with examples and etymology. Find out how common and how to pronounce degenerate in modern English.
DEGENERATE | English meaning - Cambridge Dictionary
Degenerate can be a verb, an adjective, or a noun. As a verb, it means to become worse in quality or condition. As an adjective, it means bad or immoral. As a noun, it means a morally …
DEGENERATE definition | Cambridge Learner’s Dictionary
Degenerate can be a verb, noun or adjective. As a verb, it means to become worse or decline. As a noun, it means a state of decline or deterioration. As an adjective, it means having low moral …
degenerate verb - Definition, pictures, pronunciation and usage …
Learn the meaning, pronunciation and usage of the verb degenerate, which means to become worse or lower in quality. See how to use degenerate in sentences and synonyms.
degenerate noun - Definition, pictures, pronunciation and usage …
Definition of degenerate noun in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
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