Search results

Create the page "Infinite product spaces" on this wiki! See also the search results found.

• Integer-valued calculus
  ...ings simpler. First, there are no limits. Second, the infinite-dimensional spaces of functions and forms are replaced with finite-dimensional ones. Third, th Invoking linear algebra now, we have Euclidean spaces with these generators and linear operators with these matrices:
  27 KB (3,824 words) - 19:07, 26 January 2019
• Duality: forms as cochains
  '''Exercise.''' Prove that, if the spaces are finite-dimensional, we have Therefore, by the ''Classification Theorem of Vector Spaces'', we have the following:
  29 KB (4,540 words) - 13:42, 14 March 2016
• Advanced Topology: exercises
  #Prove that $\Omega ^k({\bf R})$ is infinite dimensional. ...f discrete differential forms for the complex: [[Image:Describe the vector spaces of discrete differential forms for the complex below.png|center]]
  9 KB (1,487 words) - 18:18, 9 May 2013
• Vector spaces: introduction
  This is called ''[[scalar multiplication]]'', also known as "scalar product": Specific vector spaces:
  14 KB (2,238 words) - 17:38, 5 September 2011
• Linear Algebra by Messer
  ...s here are too terse in my opinion. I was good to see infinite dimensional spaces as an optional topic. Many good examples are given. In chapter 4, [[inner product spaces]] are introduced axiomatically. I'd prefer to put this topic at the end of
  2 KB (325 words) - 19:45, 7 March 2016
• Algebra of differential forms
  What about [[symmetry]]? That is, is it similar to the [[dot product]]: ...symmetric but [[anti-symmetric]]. That is, they are more like the [[cross product]]:
  11 KB (1,947 words) - 18:14, 22 August 2015
• New topological spaces from old
  ...en the [[product set]] $X \times Y$ becomes a topological space with the [[product topology]].</center> Infinite products are also possible.
  1 KB (199 words) - 20:20, 21 July 2011
• Lefschetz numbers in control theory
  Typically, the space of pairs of states and inputs is the product of the two: $N=M\times U.$ However nontrivial bundles are also common. For ...of $M,N,$ and $f$ is also continuous. This means that we have to consider spaces [[homeomorphic]] (or [[homotopy equivalent]]) to $M,N$ and maps [[homotopic
  17 KB (3,052 words) - 22:12, 15 July 2014
• Closed and exact forms
  Recall from [[linear algebra]], that each linear operator produces two vector spaces: ...nd use [[linearity]] later), where $dX$ is a basis $k$-form (i.e., [[wedge product]] and $A=A(x^1,...,x^n)$ is a coefficient function, twice continuously diff
  9 KB (1,423 words) - 20:53, 13 March 2013
• Cubical complex
  ...ly, a cubical cell<!--\index{cells}--> in the $N$-dimensional space is the product of vertices and edges: ...epresentation of the cube $P$. For each edge $A_i = [n_i, n_i + 1]$ in the product, we define a pair of ''opposite faces'' of $P$:
  29 KB (4,800 words) - 13:41, 1 December 2015
• Chain complexes
  *with $R={\bf R}$ (or other fields), the chain groups are vector spaces, and now <center> ''modules are vector spaces over rings''.</center>
  33 KB (5,293 words) - 03:06, 31 March 2016
• Calculus Illustrated
  8 The areas of infinite regions: improper integrals 4 Infinite series
  16 KB (1,933 words) - 19:50, 28 June 2021

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)