Vector Spaces Axiom

0.0(0)
studied byStudied by 0 people
0.0(0)
full-widthCall with Kai
GameKnowt Play
New
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/9

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

10 Terms

1
New cards

Additive Closure (AC)

v1 + v2 ∈ V

2
New cards

Scalar Closure (SC)

av1 ∈ V

3
New cards

Associativity of Addition (A1)

(v1 + v2) + v3 = v1 + (v2 + v3)

4
New cards

Commutativity of Addition (A2)

v1 + v2 = v2 + v1

5
New cards

Additive Identity Existence (A3)

0 vector ∈ V exists such that v1 + 0 vector = v1

6
New cards

Additive Inverse Existence (A4)

-v1 ∈ V exists such that v1 + (-v1) = 0 vector

7
New cards

Associativity of Scalar Multiplication (S1)

(ab)v1 = av1 +  bv1

8
New cards

Distributivity of Scalar Multiplication over Scalar Addition (S2)

(a + b)v1 = av1 +  bv1

9
New cards

Distributivity of Scalar Multiplication over Vector Addition (S3)

a(v1 +  v2) = av1 +  bv2

10
New cards

Scalar Multiplication Identity Exsistence

1v1 = v1 for all v1 ∈ V