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# Matrix Calculus

Basically derivatives and integrals of matrices parallel derivatives and integrals of ordinary functions. The easiest way to figure out what the derivative or integral will be is to expand the matrix and then take an element by element derivative or integral.

If we let x be an vector and let , where y is an vector (for example, if , where A is an matrix, then y will be an vector), then (3.12.1)

We will also include the following to our definition: (3.12.2)

and (3.12.3)

Now we'll list two very useful results.3.8 If x is an vector and A is an matrix of elements that are not functions of x, then (3.12.4)

If A is an matrix of elements that are not functions of x, then (3.12.5)

and if A is symmetric, that is , then     Next: Linear Models Up: How to ask questions Previous: General Overview   Index

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Frank Starmer 2004-05-19
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