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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.
'''Quadratic forms''' are functions expressed as multivariable equations in [[linear algebra]] that have no combined power larger than 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:
A quadratic form ''q('''x''')'' can be written as:
:''q('''x''')'' = '''''x'''''(''A'' '''''x''''')
:''q('''x''')'' = '''''x'''''(''A'' '''''x''''')
[[Category:linear algebra]]
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.
[[Category:Linear Algebra]]