EM 214 Vector Spaces

0.0(0)
Studied by 0 people
call kaiCall Kai
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/6

encourage image

There's no tags or description

Looks like no tags are added yet.

Last updated 4:59 PM on 4/18/26
Name
Mastery
Learn
Test
Matching
Spaced
Call with Kai

No analytics yet

Send a link to your students to track their progress

7 Terms

1
New cards

Vector space axioms

  1. x + y ∈ V

  2. x + y = y + x

  3. x + (y + z) = (x + y) + z

  4. x + 0 = x

  5. x + (-1)x = 0

  6. kx ∈ V

  7. k(x + y) = kx + ky

  8. (k + l)x = kx + lx

  9. k(lx) = (kl)x

  10. 1x = x

2
New cards

Set types

  • Rn = [a1, a2, …, an]

  • Rmxn is a matrix

  • Pn = a0 + a1x + … + anxn

  • C[a, b] is all continuous functions over a & b

3
New cards

Notation

knowt flashcard image
4
New cards

Subspaces

  • W is subspace of V (W ⊆ V) if:

  1. 0 ∈ W

  2. w1 + w2 ∈ W

  3. kw ∈ W

5
New cards

Basis

  • Set of vectors of V is a basis if:

  1. {v1, v2, …, vn} is linearly independant

  2. span{v1, v2, …, vn} = V

6
New cards

Span

  • span{v1, v2, …, vn} = {k1v1, k2v2, …, knvn | k1, k2, …, kn ∈ R}

  • if V = span{S} and S ⊆ V, then S spans V.

7
New cards

Dimension of basis

  • Number of vectors in a basis is called its dimension.

    • dim(Rn) = n

    • dim(Mmxn) = m x n

    • dim(Pn) = n + 1