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Physics LibreTexts

10.4: Matrix Formulation

( \newcommand{\kernel}{\mathrm{null}\,}\)

The dot product can also be written in matrix form. To begin, let's represent vectors as column vectors-that is, 3×1 matrices. We'll define the vectors A and B as the column vectors

A=(AxAyAz);B=(BxByBz)

The dot product can then be written

AB=ATB=(AxAyAz)(BxByBz)=(AxBx+AyBy+AzBz).

This the the product of a 1×3 row array with a 3×1 column array, which gives a 1×1 result (i.e. a scalar).


10.4: Matrix Formulation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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