Transcription of Vectors and Matrices A - MIT
{{id}} {{{paragraph}}}
Example: air traffic controller
Vectors and Matrices A - MIT
Vectors and Matrices Appendix A. Vectors and Matrices are notational conveniences for dealing with systems of linear equations and inequalities. In particular, they are useful for compactly representing and discussing the linear programming problem: n X. Maximize cjxj, j=1. subject to: n X. ai j x j = bi (i = 1, 2, .. , m), j=1. xj 0 ( j = 1, 2, .. , n). This appendix reviews several properties of Vectors and Matrices that are especially relevant to this problem. We should note, however, that the material contained here is more technical than is required for understanding the rest of this book. It is included for completeness rather than for background. Vectors . We begin by defining Vectors , relations among Vectors , and elementary vector operations. Definition. A k-dimensional vector y is an ordered collection of k real numbers y1 , y2 , .. , yk , and is written as y = (y1 , y2 , .. , yk ). The numbers y j ( j = 1, 2.)
A.2 Matrices 489 Definition. Two matrices A and B are said to be equal, written A = B, if they have the same dimension and their corresponding elements are equal, i.e., aij = bij for all i and j. In some instances it is convenient to think of vectors as merely being special cases of matrices.
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: