What do people mean by "canonical"? - Mathematics Stack …
2022年5月18日 · Also the concept canonical is very similar to the concept conventional but the latter is used when you must choose something that excludes other possibilities (i.e. in some context we can adopt the convention that $0^0=1$, then $0^0=0$ is excluded as a possibility), however the former is applied when you choose some standard way to apply a map ...
What is meant by canonical? - Mathematics Stack Exchange
2013年9月11日 · $\begingroup$ Canonical has a technical meaning, but here is just means the "natural basis" within the given context. For example, if working in Euclidean space the "canonical basis" would be the "standard basis" $\{e_1,\ldots,e_n\}$ with …
What is the definition of "canonical"? - Mathematics Stack Exchange
2018年8月1日 · When you have an equivalence class of objects, "canonical" refers to your favourite or the most obvious element of the equivalence class to call the class by. For example, with the equivalence classes used to define the rational numbers the canonical element is the fraction in reduced form, i.e. $\frac{1}{2}$ instead of $\frac{2}{4}$.
What is a "canonical function"? - Mathematics Stack Exchange
Canonical way to represent countable limit ordinals Hot Network Questions What is the table behind the main altar where the Sacramental wine and chalice are placed before Consecration?
Deeper meaning of "canonical"? - Mathematics Stack Exchange
2017年1月12日 · "Canonical" doesn't have a widely used technical meaning as far as I'm aware. (It does have some technical definitions, but the ones I'm aware of are not widely used.) The categorical notion that unambiguously comes closest to capturing the notion of a "canonical map" is the notion of a universal arrow. I'll use a variation on the presentation ...
What does the term "canonical problem" mean generally?
2020年9月24日 · "Canonical" means according to the canon. The canon is a standard form of hymns in orthodox churches. In mathematics it is an aphorism for "as we normally do it", a standard formulation or standard approach.
linear algebra - How do I find a canonical basis for A?
2017年8月13日 · The canonical basis for the same linear transformation is the basis in which the transformation is expressed by a matrix in the Jordan canonical form. This basis is made by the proper and generalized eigenvectors of the tranformation.
linear algebra - What is the canonical form of a matrix?
2018年2月6日 · I have been asked to find the canonical form of a matrix, but I am not exactly sure what is meant by this. I found the eigenvalues and eigenvectors of the matrix, and the solution I was shown for the canonical form is a diagonal matrix with the eigenvalues on the diagonal (the explanation for this was that the eigenvalues were distinct)--I am ...
basic difference between canonical isomorphism and isomorphims
2019年4月26日 · "Natural" and "canonical" have related but somewhat different meanings in mathematics. This doesn't mean everyone uses them perfectly in accordance to those meanings. But this is a common usage. I'll start out with "natural" first, then bring in "canonical". The term natural actually has a precise mathematical meaning, defined in Category theory.
What are canonical vectors? - Mathematics Stack Exchange
The canonical vectors are the columns 2 and 3. Okay. I only see two particular properties here: the columns only have one non-null term, and they also have a coefficient of 1. Is that what a canonical vector is?