Search results

Create the page "Matrix Algebra" on this wiki! See also the search results found.

• Inner product
  ...\cdot, \cdot >$ on an $n$-dimensional vector space $V$ can be computed via matrix multiplication where $Q$ is a positive definite, symmetric $n \times n$ matrix.
  4 KB (749 words) - 20:12, 1 May 2013
• Matrices as functions
  Turns out, this is [[matrix product]]! It is called a ''matrix representation'' of this function, $F$. But, if we do have a matrix, we can always understand it as a function, example:
  13 KB (2,187 words) - 22:17, 9 September 2011
• Functions
  ...ften given by ''formulas''. In that case, the above issue is resolved with algebra. ...t: $A$ depends on $w$ only. What is this function? With more middle school algebra, we make this function explicit:
  151 KB (25,679 words) - 17:09, 20 February 2019
• The algebra of oriented cells
  With the algebra we have learned, we can easily conclude the following about the homology of
  36 KB (6,395 words) - 14:09, 1 December 2015
• Homotopy
  as quotients of the maps of chains. However, in comparison, where is the algebra in these homotopy ''groups''? <!--200-->[[image:algebra of loops.png|center]]
  46 KB (7,846 words) - 02:47, 30 November 2015
• Linear operators: part 4
  '''Lesson:''' Linear algebra reveals the ''[[topology]]'' of the graph. ...ifferentiation \hspace{3pt}} \colon {\bf P} \rightarrow {\bf P}$. Find the matrix.
  13 KB (2,067 words) - 01:11, 12 September 2011
• Simplicial homology
  ...clear that another choice of cells' orientations will produce a different algebra of chains... but the same homology groups<!--\index{homology groups}-->! In ==The algebra of oriented chains==
  31 KB (5,170 words) - 13:44, 1 December 2015
• Duality: forms as cochains
  Linear algebra helps one appreciate this seemingly trivial relation. The answer is given b ...cating what $0, -\alpha \in V^*$ are, and then refer to theorems of linear algebra.
  29 KB (4,540 words) - 13:42, 14 March 2016
• Cohomology
  Linear algebra helps one appreciate this seemingly trivial relation. Indeed, the answer is ...cating what $0, -\alpha \in V^*$ are, and then refer to theorems of linear algebra.
  45 KB (6,860 words) - 16:46, 30 November 2015
• Topology of graphs
  ...is via its ''incidence matrix''<!--\index{incidence matrix}-->, i.e., the matrix with a $1$ in the $ij$ position if the graph contains edge $ij$ and $0$s el It is time now to start to recognize the ''need for algebra'' in topology.
  25 KB (4,214 words) - 16:08, 28 November 2015
• Test
  #[[Topology vs algebra vs geometry]] #[[Algebra of differential forms]]
  16 KB (2,139 words) - 23:01, 9 February 2015
• Forms in Euclidean spaces
  In order to simplify things, we utilize what we know about the ''algebra'' of directions on ${\bf R}$: the direction from $n$ to $n+1$ is the opposi Both approaches rely on ''the algebra of the Euclidean space''.
  44 KB (7,778 words) - 23:32, 24 April 2015
• College Algebra -- Fall 2016
  '''MTH 130 College Algebra.''' 3 hrs. Polynomial, rational, exponential, and logarithmic functions. Gr *Prerequisites: solid algebra skills, some knowledge of Cartesian coordinates, familiarity with basic fun
  10 KB (1,078 words) - 19:07, 16 December 2016
• Calculus Illustrated
  6 The algebra of exponents 11 The algebra of sums and differences
  16 KB (1,933 words) - 19:50, 28 June 2021
• Modeling with discrete exterior calculus
  ...geneous case, so for the purposes of speed of the program,the conductivity matrix was replaced with a constant $k=0.6$. ...model is isotropic. In order to do this, we take [[level curve]]s of this matrix at varying times and observe the shape of these curves. We began by taking
  31 KB (5,254 words) - 17:57, 21 July 2012
• Applied Topology and Geometry
  #[[Topology vs algebra vs geometry]] #[[Algebra of differential forms]]
  16 KB (2,088 words) - 16:37, 29 November 2014
• Homotopy and homotopy equivalence
  as quotients of the maps of chains. However, in comparison, where is the algebra in these homotopy ''groups''? [[image:algebra of loops.png|center]]
  45 KB (7,738 words) - 15:18, 24 October 2015
• The algebra of cubical cells
  ...appears twice, it is canceled. The computation is carried out as if we do algebra with ''binary arithmetic''<!--\index{binary arithmetic}-->. That's why we c With the algebra we have learned, we can easily conclude the following about these cycles:
  46 KB (7,844 words) - 12:50, 30 March 2016
• College Algebra by Ratti and McWaters
  ''College Algebra'', 2/E by J. S. Ratti and Marcus S. McWaters Used it for [[College Algebra -- Fall 2011]], see also [[College algebra: course]]. It's better than many others I've seen.
  2 KB (269 words) - 18:53, 16 November 2011
• Simplicial complexes and maps
  ==The algebra of oriented chains== Up to this point, the development of the algebra of chains follows the same path as in the case of oriented ''cubical'' comp
  27 KB (4,625 words) - 12:52, 30 March 2016

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