# A notation convenience for certain non-linear expressions

*From*: Mok-Kong Shen <mok-kong.shen@xxxxxxxxxxx>*Date*: Tue, 01 Jun 2010 13:15:35 +0200

The following is essentially commonplace and nothing special

but o.k., as I was told by a couple of mathematicians. I am

posting it nonetheless here, because I surmise it could eventually

be of some use to somebodies.

If f11(x) etc. are functions of x, one can namely e.g. use

| f11 f12 | | x1 |

| | * | |

| f21 f22 | | x2 |

to express the vector

| f11(x1) + f12(x2) |

| |

| f21(x1) + f22(x2) |

where the elements are non-linear, if the functions are so. That is,

one could in this way fairly conveniently express certain non-linear

computations using the familiar operator notations of matrix calculus

in linear algebra.

An practical example is to have full-cycle higher order permutation

polynomials mod 2^n as the functions fij, for which inverses may be

numerically computed and hence non-singular matrices may be defined.

Thanks.

M. K. Shen

.

**Follow-Ups**:**Re: A notation convenience for certain non-linear expressions***From:*Mok-Kong Shen

**Re: A notation convenience for certain non-linear expressions***From:*Tom St Denis

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