Physics Lournal

An addition operation, referred to as vector addition, which takes two vectors $u ,v\in V$ , and produces some third vector $w$ , which is equal to $u + v$ , and exists in $V, (w \in V)$ .

Worked Example: Associativity.

$\begin{pmatrix} x_1 \ x_2 \ \vdots \ x_n \end{pmatrix} + \begin{pmatrix} y_1 \ y_2 \ \vdots \ y_n \end{pmatrix} + \begin{pmatrix} z_1 \ z_2 \ \vdots \ z_n \end{pmatrix} = \begin{pmatrix} x_1 + y_1 \ x_2 + y_2 \ \vdots \ x_n + y_n\ \end{pmatrix} + \begin{pmatrix} z_1 \ z_2 \ \vdots \ z_n \end{pmatrix}$

$\begin{pmatrix} (x_1 + y_1) + z_1 \ (x_2 + y_2 ) + z_2\ \vdots \ (x_n + y_n) + z_n \ \end{pmatrix}$

$\begin{pmatrix} x_1 + (y_1 + z_1) \ x_2 + (y_2 + z_2)\ \vdots \ x_n + (y_n + z_n) \ \end{pmatrix}$

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

An addition operation, referred to as vector addition, which takes two vectors u,v∈Vu ,v\in Vu,v∈V, and produces some third vector www, which is equal to u+vu + vu+v, and exists in V,(w∈V)V, (w \in V)V,(w∈V).

Worked Example: Associativity.

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.

An addition operation, referred to as vector addition, which takes two vectors $u ,v\in V$ , and produces some third vector $w$ , which is equal to $u + v$ , and exists in $V, (w \in V)$ .

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.