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・ Quadrate pebblesnail
・ Quadrate tubercle
・ Quadrathlon
・ Quadratic
・ Quadratic (collection)
・ Quadratic algebra
・ Quadratic assignment problem
・ Quadratic bottleneck assignment problem
・ Quadratic classifier
・ Quadratic configuration interaction
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Quadratic form (statistics)
・ Quadratic formula
・ Quadratic Frobenius test
・ Quadratic function
・ Quadratic Gauss sum
・ Quadratic growth
・ Quadratic integer
・ Quadratic integral
・ Quadratic integrate and fire
・ Quadratic irrational
・ Quadratic Jordan algebra
・ Quadratic Lie algebra
・ Quadratic mean diameter
・ Quadratic pair
・ Quadratic probing


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Quadratic form (statistics) : ウィキペディア英語版
Quadratic form (statistics)

In multivariate statistics, if \epsilon is a vector of n random variables, and \Lambda is an n-dimensional symmetric matrix, then the scalar quantity \epsilon^T\Lambda\epsilon is known as a quadratic form in \epsilon.
==Expectation==
It can be shown that
:\operatorname\left()=\operatorname\left(\Sigma\right ) + \mu^T\Lambda\mu
where \mu and \Sigma are the expected value and variance-covariance matrix of \epsilon, respectively, and tr denotes the trace of a matrix. This result only depends on the existence of \mu and \Sigma; in particular, normality of \epsilon is ''not'' required.
A book treatment of the topic of quadratic forms in random variables is

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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