Difference between revisions of "Quadratic form"
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:''q('''x''')'' = '''''x'''''(''A'' '''''x''''') | :''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]] | [[Category:linear algebra]] | ||
Revision as of 18:05, May 13, 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.