- #1
Sander1337
- 10
- 0
Hi there!
My name is Sander, and I'm a (dutch) Econometrics student at the Rotterdam Erasmus University. This is my first year and I'm getting an introduction to "Matrix Algebra", which is (I think, shoot me if I'm wrong..) quite the same as Linear Algebra (since the book we use is called Linear Algebra, by David Poole).
The problem I encountered is the word span, I don't quite get what is means, and even more important; what it's results would be if I would "calculate" the span of some vectors/matrices.
The given definition of Span from my book is;
If S={v1,v2,...,vk} is a set of vectors in R^n, then the set of all linear combinations of v1,v2,...,vk is called the span of v1,v2,...,vk and is denoted by the span(v1,v2,...,vk) or span(S). If span(S)=R^n, then S is called a spanning set for R^n.
Now as I said I don't quite get what they are trying to explain, this definition doesn't give me a clear view of what this means, and so I haven't got a clue of what span means and what answer(s) span(S) would get me.
I hope you can help me out, and give me a more easy-to-use explanation of the term "span" and what the span delivers me. I've already searched with google but that didn't bring in any results.
Really hope you can help me out!
Greets,
Sander
PS: Sorry for the bad English, like Linear Algebra, following education in English is new for me as well...
My name is Sander, and I'm a (dutch) Econometrics student at the Rotterdam Erasmus University. This is my first year and I'm getting an introduction to "Matrix Algebra", which is (I think, shoot me if I'm wrong..) quite the same as Linear Algebra (since the book we use is called Linear Algebra, by David Poole).
The problem I encountered is the word span, I don't quite get what is means, and even more important; what it's results would be if I would "calculate" the span of some vectors/matrices.
The given definition of Span from my book is;
If S={v1,v2,...,vk} is a set of vectors in R^n, then the set of all linear combinations of v1,v2,...,vk is called the span of v1,v2,...,vk and is denoted by the span(v1,v2,...,vk) or span(S). If span(S)=R^n, then S is called a spanning set for R^n.
Now as I said I don't quite get what they are trying to explain, this definition doesn't give me a clear view of what this means, and so I haven't got a clue of what span means and what answer(s) span(S) would get me.
I hope you can help me out, and give me a more easy-to-use explanation of the term "span" and what the span delivers me. I've already searched with google but that didn't bring in any results.
Really hope you can help me out!
Greets,
Sander
PS: Sorry for the bad English, like Linear Algebra, following education in English is new for me as well...