diagonal quadratic form
Let be a quadratic form over a field (), where is the column vector . We write as
where is the associated symmetric matrix over . We say that is a diagonal quadratic form if is a diagonal matrix.
Let’s see what a diagonal quadratic form looks like. If is diagonal whose diagonal entry in cell is , then
So the coefficients of for are all in a diagonal quadratic form. A diagonal quadratic form is completely determined by the diagonal entries of .
Remark. Every quadratic form is equivalent (http://planetmath.org/EquivalentQuadraticForms) to a diagonal quadratic form. On the other hand, a quadratic form may be to more than one diagonal quadratic form.
Title | diagonal quadratic form |
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Canonical name | DiagonalQuadraticForm |
Date of creation | 2013-03-22 15:42:05 |
Last modified on | 2013-03-22 15:42:05 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 12 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 11E81 |
Classification | msc 15A63 |
Classification | msc 11H55 |
Synonym | canonical quadratic form |
Related topic | DiagonalizationOfQuadraticForm |