Register to reply 
Range and null space of T 
Share this thread: 
#1
Mar1010, 09:04 AM

P: 9

Given a linear transformation T from V to V, can we say that the range of T is in the space spanned by the column vectors of T. And we already know that the null space of T is the one spanned by the set of vectors that are orthogonal to the row vectors of T, then is there any general relationship b/t the range of T and the nulll space of T ?



#2
Mar1010, 10:49 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361

Yes, the "ranknullity" theorem: If T is a linear transformation from U to V then the nulliity of T (the dimension of the null space of T) plus the rank of T (the dimension of the range of T in V) is equal to the dimension of U.



Register to reply 
Related Discussions  
Null space and Column Space  Linear & Abstract Algebra  1  
Basis for null space, row space, dimension  Calculus & Beyond Homework  1  
Column Space, Null Space  Calculus & Beyond Homework  0  
Showing null space and range are invariant  Linear & Abstract Algebra  2  
Null space  Calculus & Beyond Homework  8 