“Positive Definite Quadratic Form”的概念、定义、习题解题方法及翻译-数学辞典

单词

Positive Definite Quadratic Form

释义

Positive Definite Quadratic Form

A Quadratic Form is said to be positive definite if for . AReal Quadratic Form in variables is positive definite Iff its canonical form is

(1)

A Binary Quadratic Form

(2)

of two Real variables is positive definite if it is

for any

, therefore if

and the Discriminant

. A BinaryQuadratic Form is positive definite if there exist Nonzero

and

such that

(3)

(Le Lionnais 1983).

A Quadratic Form is positive definite Iff every Eigenvalue of is Positive. A Quadratic Form with a Hermitian Matrix ispositive definite if all the principal minors in the top-left corner of are Positive, in other words

			(4)
			(5)
			(6)

See also Indefinite Quadratic Form, Positive Semidefinite Quadratic Form

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1106, 1979.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 38, 1983.

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