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• Discrete Calculus: Applied Analysis on Graphs for Computational Science by Grady and Polimeni
  p. 14. "..[[vector calculus:course|vector calculus]] -- which is defined only for up to three spacial [[dimension]]s. ...lot from a vertex to the next. "Therefore, the goal of the most filtering operations is to remove the high frequency noise, while being careful to preserve the
  11 KB (1,663 words) - 16:03, 26 November 2012
• Products of vector spaces
  ...airs (a,b) of elements in X and Y respectively, as a vector space with the operations '''Theorem.''' (1) The [[basis of vector space|bases]] of L and M form a basis of L×M.
  613 bytes (129 words) - 14:24, 4 April 2010
• Relative topology
  ...that for vector spaces (or groups) the subset needs to be closed under the operations while for topological spaces a subset can ''always'' be seen as a subspace. ...' extension of a linear operator $f:A\to W$ to $F:V\to W$, where $V,W$ are vector spaces and $A$ is a subset of $V$.
  34 KB (6,089 words) - 03:50, 25 November 2015
• Homology of images
  The homology groups of this image are [[vector space]]s generated by these [[cycle]]s, as follows. Consider first the imag ...ond, as we shall see shortly, this approach allows us to perform algebraic operations with cycles.
  2 KB (282 words) - 12:25, 12 August 2015
• Vector space of infinite sequences
  1. Is this a [[vector space]] in some sense? So the operations are well defined.
  2 KB (319 words) - 02:56, 13 October 2011
• MATLAB
  <p>.. the matrix/vector/tensor core is very elegant and powerful.</p> ...tions, they can’t be analyzed as matrices as they aren’t subject to matrix operations. They are in fact tables.</p>
  4 KB (548 words) - 14:55, 9 October 2010
• Fields related to computer vision
  Let’s start with “dual purpose” image processing tasks. These operations are also image analysis tools: ...r [[Robustness of topology]] (specifically, robustness under morphological operations).</li>
  9 KB (1,379 words) - 01:26, 22 February 2011
• Algebraically closed
  ...]], [[ring]] etc, a subset A of X is ''algebraically closed'' if algebraic operations on the elements of A won't result in elements outside of A. Then A is also a group, vector space, etc.
  349 bytes (54 words) - 01:24, 25 March 2011
• Parametric complexes
  '''Exercise.''' Prove that the two definitions produce isomorphic vector spaces for homology over ${\bf R}$. However, since the persistence can decrease under algebraic operations, the elements of high persistence do not, in general, form a subgroup of th
  45 KB (7,255 words) - 03:59, 29 November 2015
• Subspace of vector space
  ...$V$, any subset $U$ of $V$ that is also a vector space with respect to the operations of $V$ is called ''linear subspace'' or simply ''subspace''.
  200 bytes (33 words) - 01:07, 19 February 2011
• Linear Algebra by Messer
  ...some context for the student. I was glad to see [[quotient space]]s and [[vector field]]s as optional topics. ...is, again, no context. Meanwhile, spending so much time on elementary row operations seems wasteful.
  2 KB (325 words) - 19:45, 7 March 2016
• More metric complexes
  ...sets of $|K|$ form a $\sigma$-algebra, i.e., a collection closed under the operations of complement, countable union, and countable intersection. If, furthermore ...ood as the angle between the direction vector of the former and the normal vector of the latter.
  21 KB (3,445 words) - 13:53, 19 February 2016
• Elementary Linear Algebra -- Spring 2018
  ...Linear Algebra.''' Systems of linear equations, matrices and determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications *Outcomes: the student will learn vector algebra and matrix algebra and how to apply them.
  4 KB (573 words) - 13:07, 7 April 2018
• Geometric complexes
  ...sets of $|K|$ form a $\sigma$-algebra, i.e., a collection closed under the operations of complement, countable union, and countable intersection. If, furthermore ...ood as the angle between the direction vector of the former and the normal vector of the latter.
  20 KB (3,354 words) - 17:37, 30 November 2015
• Vector space
  There are two operations: addition of two vectors and multiplication of a vector by a scalar. The satisfy the following axioms:
  478 bytes (111 words) - 21:08, 11 September 2009
• Is the intersection of two linear subspaces always a linear subspace?
  ...near subspace iff A is [[algebraically closed|closed]] under the algebraic operations of V. But the intersection of two algebraically closed subsets is closed...
  613 bytes (96 words) - 23:35, 18 November 2010
• Linearity
  Preserving vector operations:
  450 bytes (72 words) - 14:26, 30 July 2012
• Image processing
  ...o images as [[matrices]]. The reason is that we will not perform algebraic operations with images. Matrices will appear elsewhere in the context of [[homology th ...pixel there assigned 3 integers. One can think of a ''color image'' as a 3-vector attached to each pixel or as 3 tables of integers, etc. For more see [[Colo
  5 KB (798 words) - 15:16, 25 November 2010
• Derivative
  [[Image:best affine approximation vector.jpg|right]] In this section we'll see how the derivative is affected by [[vector operations]].
  4 KB (659 words) - 01:47, 30 August 2010
• Applications of differential calculus
  ...sions? Below are the possible types of limits that correspond to algebraic operations: [[image:vector field R1.png| center]]
  59 KB (10,063 words) - 04:59, 21 February 2019

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