Difference between revisions of "Rank-nullity theorem"

Revision as of 05:13, May 9, 2010

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.

@@ Line 5: / Line 5: @@
 Using the concept of [[dimension]], the above formula can be rewritten as:
-:dim([[kernel]] ''A'') + dim([[image]] ''A'') = ''m''
+:dim([[kernel]] ''A'') + dim([[image (mathematics)|image]] ''A'') = ''m''
 This sometimes called the fundamental theorem of linear algebra.
 [[Category:linear algebra]]