Physics Lournal

A scalar multiplication operation that takes some scalar $c$ , which is an element of $F$ , ( $c \in F$ ), and a vector $v \in V$ , and produces a new vector $w$ , which is equal to $c(v)$ , and exists in $\small V, (w \in V)$ .

$c\begin{pmatrix} x_1 \ x_2 \ \vdots \ x_n \end{pmatrix} = \begin{pmatrix} c(x_1) \ c(x_2) \ \vdots \ c(x_n) \end{pmatrix} = \begin{pmatrix} cx_1 \ cx_2 \ \vdots \cx_n \end{pmatrix} = w$ .

Referenced in

Linear Map

In Mathematics, a linear map, is a mapping $V \rightarrow W$ , between two vector spaces, that preserves the results of the operations of vector addition, and scalar multiplication.

Vector Space

A scalar multiplication operation that takes some scalar ccc, which is an element of FFF, (c∈Fc \in Fc∈F), and a vector v∈Vv \in Vv∈V, and produces a new vector www, which is equal to c(v)c(v)c(v), and exists in V,(w∈V)\small V, (w \in V)V,(w∈V).

Referenced in

Linear Map

In Mathematics, a linear map, is a mapping V→WV \rightarrow WV→W, between two vector spaces, that preserves the results of the operations of vector addition, and scalar multiplication.

A scalar multiplication operation that takes some scalar $c$ , which is an element of $F$ , ( $c \in F$ ), and a vector $v \in V$ , and produces a new vector $w$ , which is equal to $c(v)$ , and exists in $\small V, (w \in V)$ .

In Mathematics, a linear map, is a mapping $V \rightarrow W$ , between two vector spaces, that preserves the results of the operations of vector addition, and scalar multiplication.