216.66.5.43: /* Calculating the cophenetic correlation coefficient */ Using a bar to indicate averages

2014-02-07T15:23:44Z

Calculating the cophenetic correlation coefficient: Using a bar to indicate averages

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	~~== Fundamental Matrix in Linear Systems ==~~		Hello and welcome. My name is Irwin and I completely dig that title. For many years he's been working as a receptionist. One of the issues he enjoys most is ice skating but he is having difficulties to find time for it. Puerto Rico is where he and his spouse reside.<br><br>Here is my blog post ... [http://carnavalsite.com/demo-page-1/solid-advice-in-relation-to-yeast-infection/ http://carnavalsite.com/]
	~~The fundamental matrix of <math> \dot{x}(t) = A(t) x(t) </math>~~ is ~~the matrix <math> \Psi </math> such~~ that ~~the n columns are linearly independent solutions of <math> \dot{x}(t) = A(t) x(t) </math>~~.

	~~By definition~~

	~~<math>~~
	~~\dot{\Psi}(t) = A(t) \Psi(t)~~
	~~</math>~~

	i.e. ~~<math> \Psi </math>~~ is ~~a fundamental matrix of <math> \dot{x}(t) = A(t) x(t) </math> if and only if <math> \dot{\Psi}(t) = A(t) \Psi(t) </math>~~ and <~~math~~> ~~\Psi~~ <~~/math~~> is ~~a non-singular matrix for all <math> t </math>~~.
	~~<ref>Chi-Tsong Chen~~. ~~1998~~. ~~Linear System Theory and Design (3rd ed~~.~~). Oxford University Press, Inc., New York, NY, USA. <~~/~~ref>~~

	~~==References==~~
	~~{{Reflist}}~~

	~~A '''fundamental matrix''' may refer~~ to

	* [[fundamental matrix (computer vision)]]
	* [[fundamental matrix (linear differential equation)]]
	* [[fundamental matrix (absorbing markov chain)]]

	~~{{disambig}}~~

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61.246.216.100: /* External links */

2012-07-23T07:04:31Z

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== Fundamental Matrix in Linear Systems ==
The fundamental matrix of <math> \dot{x}(t) = A(t) x(t) </math> is the matrix <math> \Psi </math> such that the n columns are linearly independent solutions of <math> \dot{x}(t) = A(t) x(t) </math>.

By definition

<math>
\dot{\Psi}(t) = A(t) \Psi(t)
</math>

i.e. <math> \Psi </math> is a fundamental matrix of <math> \dot{x}(t) = A(t) x(t) </math> if and only if <math> \dot{\Psi}(t) = A(t) \Psi(t) </math> and <math> \Psi </math> is a non-singular matrix for all <math> t </math>.
<ref>Chi-Tsong Chen. 1998. Linear System Theory and Design (3rd ed.). Oxford University Press, Inc., New York, NY, USA. </ref>

==References==
{{Reflist}}

A '''fundamental matrix''' may refer to

* [[fundamental matrix (computer vision)]]
* [[fundamental matrix (linear differential equation)]]
* [[fundamental matrix (absorbing markov chain)]]

{{disambig}}

{{Short pages monitor}}

Cophenetic correlation - Revision history

216.66.5.43: /* Calculating the cophenetic correlation coefficient */ Using a bar to indicate averages

61.246.216.100: /* External links */