Torsional Vibration of Turbomachinery
Including application case studies and in-depth interpretation of computer-generated results, this book offers practical answers to preventing excessive damage, failure and noise due to vibrations in machines.
TABLE OF CONTENTS Torsional Vibration of Turbomachinery
Appendix D: Introduction to Matrix Algebra
The material in this appendix is provided for readers who need refreshment on matrix algebra necessary to understand the matrix manipulations given in the theory development in Chaps. 6 through 8.
Definitions
A matrix is a rectangular array of real or complex numbers or functions. An m n matrix has m rows and n columns with a total of m n elements. A matrix that has the same number of rows and columns is called a square matrix.
A matrix called A is usually written as [ A] or when it is not ambiguous, simply as A. An m n matrix [ A] would have the following form:
Two matrices are equal only if all their element values are equal.
A matrix V would be called a column vector if it had only a single column ( n = 1) and would be written as { V} to distinguish it, or as [ V] with some elements defined. Similarly, a row matrix W has a single row ( m = 1) and would be written as [ W].
Some square matrices have only nonzero elements on their main diagonals and are logically referred to as diagonal matrices. The main diagonal runs from the upper left corner of the matrix to the bottom right, and the elements on it therefore have equal row and column subscripts.
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