Difference between revisions of "Quadratic form"
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| − | + | {{move|quadratic form}} | |
| − | + | '''Quadratic forms''' are functions expressed as multivariable equations in [[linear algebra]] that have only combined power of two. When represented by [[matrices]], they have a geometric significance as a shift or transformation in coordinates. | |
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| − | + | A quadratic form ''q('''x''')'' can be written as: | |
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| − | A | + | :''q('''x''')'' = '''''x'''''(''A'' '''''x''''') |
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| − | + | where '''''y''''' = ''A'' '''''x''''' is the vector resulting from multiplying a matrix and a vector (a [[linear transformation]]) and '''''x''''' ('''''y''''') is the [[scalar product]] of vectors. | |
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| − | + | [[Category:linear algebra]] | |
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Revision as of 13:02, August 11, 2010
- It has been proposed that this page, :Quadratic form, be titled, "quadratic form".
Quadratic forms are functions expressed as multivariable equations in linear algebra that have only combined power of two. When represented by matrices, they have a geometric significance as a shift or transformation in coordinates.
A quadratic form q(x) can be written as:
- q(x) = x(A x)
where y = A x is the vector resulting from multiplying a matrix and a vector (a linear transformation) and x (y) is the scalar product of vectors.