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September 7th, 2019, 10:38 AM  #1  
Newbie Joined: Sep 2019 From: Afghanistan Posts: 1 Thanks: 0  Confusion about span in Linear Algebra
Hi there, this is my first post here. I am currently studying some control theory related stuff and its basically linear algebra. However, I have some problems. I have given this exercise on which I already got an answer in Mathematics Stackoverflow: Quote:
Quote:
$$ M=\left[\begin{array}{cc}{U_{1}} & {U_{2}}\end{array}\right]\left[\begin{array}{cc}{\Sigma_{1}} & {0} \\ {0} & {0}\end{array}\right]\left[\begin{array}{c}{V_{1}^{\prime}} \\ {V_{2}^{\prime}}\end{array}\right] $$ $$ \text { Nullspace: } \mathcal{N}=\operatorname{span}\left[V_{2}\right] $$ $$ \operatorname{image}(M)=\operatorname{span}\left[U_{1}\right] $$ If I got this right the span is the spanning set of a matrix. I see how I get it despite a lack of intuition about it. What I don't get is why the are writing those indices. Isn't $V_2$ a vector? Whats the span of a vector and why the second one? The same for $U$. The answer I received and this definition are somehow similar but not identical. The answer mentions a set of vectors whilst this definition is about the span of a (single) vector. I am a little bit confused. Thank you guys. I am looking forward to be part of this community Regards, Bob  

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algebra, confusion, linear, span 
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