Definition:Orthogonal Basis of Vector Space

This page is about orthogonal basis of vector space. For other uses, see orthogonal.

Definition

Let $V$ be a vector space.

Let $\BB = \tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ be a basis of $V$.

Then $\BB$ is an orthogonal basis if and only if $\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n$ are pairwise perpendicular.

Also see

• Results about orthogonal bases of vector spaces can be found here.

Sources

• 1992: Frederick W. Byron, Jr. and Robert W. Fuller: Mathematics of Classical and Quantum Physics ... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.2$ The Resolution of a Vector into Components
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): orthogonal basis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): orthogonal basis
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): orthogonal basis