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Difference between revisions of "Rank-nullity theorem"

(This sometimes called the fundamental theorem of linear algebra.)
 
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:(rank of ''A'') + (nullity of ''A'') = ''m''
 
:(rank of ''A'') + (nullity of ''A'') = ''m''
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Using the concept of [[dimension]], the above formula can be rewritten as:
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:dim([[kernel]] ''A'') + dim([[image (mathematics)|image]] ''A'') = ''m''
  
 
This sometimes called the fundamental theorem of linear algebra.
 
This sometimes called the fundamental theorem of linear algebra.
  
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[[Category:linear algebra]]
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[[Category:Linear Algebra]]

Latest revision as of 14:35, July 28, 2016

The rank-nullity theorem states that for any n x m matrix A:

(rank of A) + (nullity of A) = m

Using the concept of dimension, the above formula can be rewritten as:

dim(kernel A) + dim(image A) = m

This sometimes called the fundamental theorem of linear algebra.

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