Re: What is Orthogonal (Exactly)?

In Linear Algebra 101, we learned that orthogonal means that two "vectors" in an "inner-product space" are "orthogonal" if and only if the inner product of the two vectors is 0. An example of an inner product space is the space of 3-D vectors where the inner product is the well-known "dot-product". There are other inner product spaces (sine waves and Fourier transformations, exponential functions, Hilbert spaces, etc) with their own vector definitions and inner-product definitions.

Practically speaking, it means that two "vectors" are "independent".

Cheers, Jay

"James" <jraustin1_at_hotmail.com> wrote in message news:a6e74506.0206150808.5d42abd4_at_posting.google.com...
> I would like to know what orthogonal means as exactly as possible.
> And what is the minimum number of thing(s) required in the concept of
> orthogonality. The following definition from searchStorage.com as a
> seed for dicussion:
>
> [ In geometry, orthogonal means "involving right angles" (from Greek
> ortho, meaning right, and gon meaning angled). The term has been
> extended to general use, meaning the characteristic of being
> independent (relative to something else). It also can mean:
> non-redundant, non-overlapping, or irrelevant. In computer
> terminology, something - such as a programming language or a data
> object - is orthogonal if it can be used without consideration as to
> how its use will affect something else.
>
> In itself, a programming language is orthogonal if its features can be
> used without thinking about how that usage will affect other features.
> Pascal is sometimes considered to be an orthogonal language, while C++
> is considered to be a non-orthogonal language. ]
>
> TIA
Received on Fri Jul 05 2002 - 21:38:49 CEST