Is a Nullspace Spanned by One Vector Possible?

tandoorichicken
Messages
245
Reaction score
0
Is it possible for a nullspace to be spanned by only one vector? Does a statement like Nul A = Span{\vec{v}_1} even have any meaning?
 
Physics news on Phys.org
Why not?...
For example, what is the nullspace of:
\left(\begin{array}{ccc}<br /> 1 &amp; 0 &amp; 0\\<br /> 0 &amp; 1 &amp; 0\\<br /> 0 &amp; 0 &amp; 0\end{array}\right)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Intro to Linear Algebra - Nullspace of Rank 1 Matrix
Replies
8
Views
2K
Tricky Problem: Prove range T = null ##\phi## when null T' has dim 1
Replies
8
Views
1K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
Replies
15
Views
2K
Vector space of functions from finite set to real numbers
Replies
17
Views
4K
Does the Null Space of a 2x3 Matrix Determine its Column Space?
Replies
15
Views
2K
Finding a complementary subspace ##U## | Linear Algebra
Replies
4
Views
2K
Span and Vector Space: Understanding Vectors in Linear Algebra
Replies
4
Views
2K
Does a Nullspace Spanned by the Zero Vector Indicate Its Dimension Is Zero?
Replies
1
Views
1K
Direct Proof that every zero of p(T) is an eigenvalue of T
Replies
24
Views
3K
Conditions for Strict Inequality in Span Intersection
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top