Difference between revisions of "Quadratic form"
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| − | + | '''Quadratic form''' is a function expressed as a multivariable equation in [[linear algebra]] that has only combined power of two. When represented by [[matrices]], it has 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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Latest revision as of 14:35, July 28, 2016
Quadratic form is a function expressed as a multivariable equation in linear algebra that has only combined power of two. When represented by matrices, it has 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.