scalar. For example, if
v¼2
0
1
3
1
2
6
(^66)
6
6
4
3
7
(^77)
7
7
5
ands¼2, then
sv¼
4
0
2
6
2
2 6 6 6 6 6 4
3 7 7 7 7 7 5
:
Division of a vector by a scalar is analogous.
B. Addition of Vectors
The addition of two vectors is the vector resulting from adding their corre-
sponding components. For example:
3
0
2
02
6
6
6
4
3
7
7
7
5
þ0
1
2
1
2
6
6
6
4
3
7
7
7
5
¼
3
1
4
1
2
6
6
6
4
3
7
7
7
5
:
Only vectors with the same number of components can be added.
Acknowledgments
This manuscript was completed while I was a Fellow at the Center for Advanced Study in the Be-
havioral Sciences in 1993–1994. I am grateful for support from the National Science Foundation
(DBS-9222358 and SES-9022192) and for valuable comments from Diana Raffman, Carol Krumhansl,
Eugene Narmour, Caroline Palmer, Einar Mencl, Subhobrata Mitra, Mark McNellis, and Denise
Vargas.
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Neural Nets, Temporal Composites, and Tonality 477