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Line 12: ==Example== As an example, let {{<math~~\|1=''~~>V'' = \mathbb{R}~~<sup>~~^2 </~~sup~~math>}}, and consider the quadratic form :<math>Q(x)=c_1{x_1}^2+c_2{x_2}^2 \,</math> where {{math\|1=''x'' = (''x''<sub>1</sub>, ''x''<sub>2</sub>)}} and {{math\|''c''<sub>1</sub>}} and {{math\|''c''<sub>2</sub>}} are constants. If {{math\|1=''c''<sub>1</sub> > 0}} and {{math\|1=''c''<sub>2</sub> > 0}}, the quadratic form {{math\|''Q''}} is positive definite. If one of the constants is positive and the other is zero, then {{math\|''Q''}} is positive semidefinite. If {{math\|1=''c''<sub>1</sub> > 0}} and {{math\|1=''c''<sub>2</sub> < 0}}, then {{math\|''Q''}} is indefinite.

Definite quadratic form: Difference between revisions