Definition:Orthogonal (Linear Algebra)/Real Vector Space
< Definition:Orthogonal (Linear Algebra)(Redirected from Definition:Orthogonal Vectors)
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Definition
Let $\mathbf u$, $\mathbf v$ be vectors in $\R^n$.
Then $\mathbf u$ and $\mathbf v$ are said to be orthogonal if and only if their dot product is zero:
- $\mathbf u \cdot \mathbf v = 0$
As Dot Product is Inner Product, this is a special case of the definition of orthogonal vectors.
Also see
Sources
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.3$ Scalar or Dot Product
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): orthogonal vectors
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): orthogonal vectors
- For a video presentation of the contents of this page, visit the Khan Academy.