Definition:Cartesian Product of Real Vector Spaces
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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