-
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 +...
- 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...
- 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...
- mathematics, a
vector bundle is a
topological construction that
makes precise the idea of a
family of
vector spaces parameterized by
another space X {\displaystyle...
-
transformation on a
general contravariant four-
vector X (like the
examples above),
regarded as a
column vector with
Cartesian coordinates with
respect to...
-
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...
- of a
random vector X {\displaystyle \mathbf {
X} } is
typically denoted by K
X X {\displaystyle \operatorname {K} _{\mathbf {
X} \mathbf {
X} }} , Σ {\displaystyle...
- of a
vector space with an
inner product is due to
Giuseppe Peano, in 1898. An
inner product naturally induces an ****ociated norm, (denoted |
x | {\displaystyle...
- In
vector calculus, the
gradient of a scalar-valued
differentiable function f {\displaystyle f} of
several variables is the
vector field (or
vector-valued...
