AMETRICS AND NULL VECTORS

A vector space Figure does not necessarily have metric properties: it may not be possible to measure and compare arbitary lengths and angles of vectors. For that, we need an inner product. This does not need to be Euclidean.

A.1 THE BILINEAR FORM

In mathematics, the metric properties are usually introduced through a bilinear form that encapsulates the measurement of all lengths in that space in a concise manner. As its name implies, a bilinear form has two arguments and is linear in each of them; the word “form” is mathematical jargon for “scalar-valued function.” The bilinear form Q of the vector space is therefore a bilinear ...

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