-
operations of
vector addition and
scalar multiplication must
satisfy certain requirements,
called vector axioms. Real
vector spaces and
complex vector spaces...
- ={\begin{pmatrix}
x_{1}\\
x_{2}\\\vdots \\
x_{n}\end{pmatrix}}} onto the
column vector y = A (
x ) = ( a 11
x 1 + ⋯ + a 1 n
x n a 21
x 1 + ⋯ + a 2 n
x n ⋮ a m 1
x 1 +...
- physics, and engineering, a
Euclidean vector or
simply a
vector (sometimes
called a
geometric vector or
spatial vector) is a
geometric object that has magnitude...
- example,
x = [
x 1
x 2 ⋮
x m ] . {\displaystyle {\boldsymbol {
x}}={\begin{bmatrix}
x_{1}\\
x_{2}\\\vdots \\
x_{m}\end{bmatrix}}.} Similarly, a row
vector is a...
- of a
random vector X {\displaystyle \mathbf {
X} } is
typically denoted by K
X X {\displaystyle \operatorname {K} _{\mathbf {
X} \mathbf {
X} }} , Σ {\displaystyle...
-
transformation on a
general contravariant four-
vector X (like the
examples above),
regarded as a
column vector with
Cartesian coordinates with
respect to...
-
vectors X {\displaystyle \mathbf {
X} } and Y {\displaystyle \mathbf {Y} } is
typically denoted by K
X Y {\displaystyle \operatorname {K} _{\mathbf {
X}...
-
indicator vector,
characteristic vector, or
incidence vector of a
subset T of a set S is the
vector x T := (
x s ) s ∈ S {\displaystyle
x_{T}:=(
x_{s})_{s\in...
- such that for
every vector x ∈
X , {\displaystyle
x\in
X,} c q (
x ) ≤ p (
x ) ≤ C q (
x ) . {\displaystyle cq(
x)\leq p(
x)\leq Cq(
x).} The
relation " p...
-
quantized separately.
Consider a k-dimensional
vector [
x 1 ,
x 2 , . . . ,
x k ] {\displaystyle [
x_{1},
x_{2},...,
x_{k}]} of
amplitude levels. It is compressed...
