Customer Reviews

Multidimensional Analysis: Algebras and Systems for Science and Engineering

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Interesting book, but it could have used a bit more fleshing out.

Chapters 0, and 8 discuss dimensions of measurement and why keeping track of units is important.

Chapter 1 makes assumption that dimensional measurements form a mathematical group and discusses some properties he thinks the group should have. I was hoping for a full explication on the groups that could work here, but was directed to the referencs.

Chapters 2, 3, and 4 derive a consistent linear algebra with his group elements as entries. The assumptions in chapter 1 could be done away with if he added a couple of words about how linear algebra would work over any group.

Chapter 7 should come after chapter 4. It discussed how traditional dimensional analysis problems like the pendulum might scale up to matrix operations. He shoots himself in the foot by saying that the Hadamard product is irrelevant to multidimensional analysis, when the dimensional inverse that he defines in chapter 2 and then uses on nearly every page is the transpose of the Hadamard inverse. Developing that observation could have been very insightful.

Chapeter 5 discusses the primary application as systems theory. Some better groundwork of the basics of system theory and some examples of setting dimensioned problems up as systems would have been appreciated.

Chapter 6 is about how to program the neccesary mathematics into a computer circa 1995. It should have been in an appendix or dropped altogether.