My Notes
Search
CTRL + K
My Notes
Search
CTRL + K
Linear Algebra
Sections
Basis
Coordinate Representation
Def Linear Combination and Span
Diagonalizability
fdvs
Inner Product Space
Internal Direct Sums
Isometry
Isomorphisms
Linear Independence
Linear Transformations
Norm
Projection
Subspace test
Vector Space Axioms
Vector Space Properties
Linear Algebra
Vector Calc
Sections
Arc Length
Basic Topology in Euclidean Spaces
Change of Variables
Differentiation
Double Integral Over a Rectangle
Double Integral Over Elementary Regions
Green's Theorem
Implicit Function Theorem
Limits and Continuity
Line Integral
Local Extremums of Real-Valued Functions
Path Integral
Surfaces and Stokes Theorem
Types of Functions
Vector Fields
Vector Calc
Welcome
Vector Space Properties
based on
Vector Space Axioms
Let
V
be a vector space, with
u
,
v
,
w
∈
V
and
c
∈
R
:
If
u
+
v
=
u
+
w
then
v
=
w
c
v
=
0
if and only if
c
=
0
or
v
=
0
(
−
1
)
v
=
−
v
(
−
c
)
v
=
−
(
c
v
)
=
c
(
−
v
)
The zero vector is unique
If
v
∈
V
its additive inverse
−
v
is unique