Definition:Cartesian Product of Real Vector Spaces

Definition

Let $V_1$ and $V_2$ be real vector spaces.

The cartesian product of $V_1$ and $V_2$ is the real vector space where:

vector addition is defined as:

$\tuple {x_1, x_2} + \tuple {y_1, y_2} := \tuple {x_1 + x_2, y_1 + y_2}$

scalar multiplication is defined as:

$\lambda \tuple {x, y} := \tuple {\lambda x, \lambda y}$

Also see

• Results about cartesian products can be found here.

Source of Name

This entry was named for René Descartes.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cartesian product
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cartesian product