Definition:Square of Vector Quantity
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Definition
Let $\mathbf u$ be a vector.
Let $\mathbf u \cdot \mathbf u$ denote the dot product of $\mathbf u$ with itself.
Then $\mathbf u \cdot \mathbf u$ can be referred to as the square of $\mathbf u$ and can be denoted $\mathbf u^2$.
Also known as
The square of $\mathbf u$ is also seen referred to as the self-product of $\mathbf u$.
Also see
- Dot Product of Vector with Itself, demonstrating that $\mathbf u^2 = u^2$, where $u$ denotes the magnitude of $\mathbf u$.
Sources
- 1927: C.E. Weatherburn: Differential Geometry of Three Dimensions: Volume $\text { I }$ ... (previous) ... (next): Introduction: Vector Notation and Formulae: Products of Vectors
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $2$. The Scalar Product: $(2.4)$
- 1957: D.E. Rutherford: Vector Methods (9th ed.) ... (previous) ... (next): Chapter $\text I$: Vector Algebra: $\S 2$