The following is definition C.7 from Appendix C (Linear Spaces Review) of Introduction to Laplace Transforms and Fourier Series, Second Edition, by Phil Dyke:
Shouldn't that be $1 \le i, j \le n$? Is it a typo?
And, of course, the $a_r \not= 0$ should be typeset to $\mathbf{a}_r \not= 0$?
Community wiki answer so that the question can be marked as answered:
As has already been clarified in the comments, these are both errors.