Difference between revisions of "What is matrix rank and how do i calculate it?"

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--[[User:Fuller|Sawyer Fuller]] 16:22, 29 October 2007 (PDT)
 
--[[User:Fuller|Sawyer Fuller]] 16:22, 29 October 2007 (PDT)
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[[Category: CDS 101/110 FAQ - Lecture 5-1]]
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[[Category: CDS 101/110 FAQ - Lecture 5-1, Fall 2007]]

Revision as of 23:24, 29 October 2007

The rank of a matrix A is the number of independent columns of A. A square matrix is full rank if all of its columns are independent. That is, a full rank matrix has no column vector v_{i} of A that can be expressed as a linear combination of the other column vectors v_{j}\neq \Sigma _{{i=0,i\neq j}}^{{n}}a_{i}v_{i}.


A simple test for determining if a matrix is full rank is to calculate its determinant. If the determinant is zero, there are linearly dependent columns and the matrix is not full rank. Prof. John Doyle also mentioned during lecture that one can perform the singular value decomposition of a matrix, and if the lowest singular value is near or equal to zero the matrix is likely to be not full rank ("singular").

--Sawyer Fuller 16:22, 29 October 2007 (PDT)