Chapter 2 Flashcards Preview

Linear Algebra > Chapter 2 > Flashcards

Flashcards in Chapter 2 Deck (15)
Loading flashcards...
1

Definition of span

We say that a list of vectors in a vector space V, spans V if every vector v element of V is a linear combination of the list of vectors

2

Definition of linear independence

A list of vectors in a vector space V is called linearly independent iff
The equation ( kv1+ bla bla bal) = nul vector

Only has the trivial solution.

3

Definition of a basis

A list of vectors B= (e1, ... , en) in a vector space V is called a basis for V iff it spans V and is linearly independent

4

Sifting lemma?

If a list of vectors spans a vector space V, then sifting the list will result a basis for V.

5

What is a coordinate vector?

Let B be a basis for a vector space V, and let v element of V,

[v]B = coln

6

Rules of Coordinate vectors?

Bl3

7

What is a change of basis matrix?

Bl3

8

Change of basis theorem?

Bl4

9

Linear Combination of preceding vectors, which statements are equivalent?

The list of vectors is linearly dependent.

Either v1=0 or for some r element of {2,3,...,n} vr is a linear combination of v1, v2,..., vr-1

10

Bumping off proposition

Bl6

11

Write down the basis for Polyn

Bl 7

12

Write down the basis for Trign

Bl7

13

Write down the basis for Matn,m

Bl7

14

Let W be a subspace of a finite dimensional vector space V, then W is finite-dimensional, and Dim(W)<= Dim(V)

Prove this

Bl8

15

Poly is infinite dimensional

Prove this

Bl9