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In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "canonical" and "normal ...
Jul 25, 2023 · Under similarity the canonical matrices, called Jordan canonical matrices, are block triangular with upper triangular “Jordan” blocks on the main diagonal. In this short chapter we are going to define these Jordan blocks and prove that every matrix is similar to a Jordan canonical matrix. Here is the key to the method.
Nov 11, 2008 · A canonical form means that values of a particular type of resource can be described or represented in multiple ways, and one of those ways is chosen as the favored canonical form. (That form is canonized, like books that made it into the bible, and the other forms are not.) A classic example of a canonical form is paths in a hierarchical file ...
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Jul 26, 2023 · The Jordan canonical form is a refinement of this theorem. The proof we gave of ( [eq:11_2Jordan]) is matrix theoretic because we wanted to give an algorithm for actually finding the matrix P P. However, we are going to employ abstract methods here. Consequently, we reformulate Theorem [thm:032952] as follows:
Jordan canonical form is a representation of a linear transformation over a finite-dimensional complex vector space by a particular kind of upper triangular matrix. Every such linear transformation has a unique Jordan canonical form, which has useful properties: it is easy to describe and well-suited for computations. Less abstractly, one can speak of the Jordan canonical form of a square matrix; every square matrix is similar to a unique matrix in Jordan canonical form, since …
