Indefinite Form

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Indefinite Form


a concept in linear algebra. The quadratic form

with real coefficients a, ij is called an indefinite form if it takes on positive and negative values for real values of the variables. By a linear change of variables, we can reduce an indefinite quadratic form to a form

For a given indefinite form the values of s and t are independent of the method of reduction of that form to the form (*) (this result is called the law of inertia of quadratic forms). The indefinite form

x2 + y2 + z2c2t2

plays an important role in special relativity. Indefinite quadratic forms occur in the study of extrema of functions of several variables, in mechanics, and in analytic geometry.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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References in classic literature ?
On his head there was a wreck of a hat of indefinite form, but his gun of a new patent was a perfect gem, and his game bag and cartridge belt, though worn, were of the very best quality.
Subsequently, rap is also detourned, as many of its most questionable features--namely, a narcissistic individualism and, above all, a flagrant machismo--subside into a more oblique and indefinite form of speech, one that also, moreover, embodies resistance as an autonomous form of creation.
Adjectives in the attributive position in Croatian, as in the majority of Slavic languages, can appear in two different forms--the definite and the indefinite form (e.g.
Mood and movement are central to all of them, whether it be the sweeping motion of flood water that carries with it an indefinite form suggesting an amalgam of objects swept together being turned over and over; the slight lifting of petals in a breeze from an open window; or butterflies, which gives the impression of them emerging from the cocoon to flutter their wings.
Note that he uses the indefinite form of the noun in bi-tamamin and the definite (with the article) in bi-l-nuqsani.
Note that only English uses an indefinite form here (a geographer in [50] and a rite in [51]) without inserting an additional demonstrative element in a construction such as "what is that/this x?" The other languages do employ such a construction, in combination with an indefinite form (French in both sentences and German in [50b]) or even in combination with a definite form (Hungarian in both sentences).
Bearing vestiges of the human body, this hauntingly indefinite form can be read as a kind of enigmatic memento mori; David seems to be exploring the depressive aspects of process painting, along with its aggressive tendencies.
(12) The first time the reader encounters the first person plural is more than two-thirds of the way through the novel, and Montalbetti's choice of possessive adjective is almost jarring in a text, which, until that point, has been dominated by indefinite forms. Inevitably, her description of "[une] chambre ou notre Simon [est] en chaussettes a genoux devant la table basse" (52) catches the reader by surprise.
The Impressionists knew this is the way the eye sees and painted vague, indefinite forms surrounding the focal point.

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