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An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site,

In the agency’s guidance on preparing workplaces for COVID-19, the Occupational Safety and Health Administration (OSHA) has categorized job functions into four risk exposure levels. We’ve fleshed out these four divisions in the following paragraphs. When you’re determining what probability values would be useful to set for your risk matrix, it’s a good idea to use these 4 categories as a starting point.

To start, I'll be a little more precise: every matrix corresponds to a weighted bipartite graph. By "graph" I mean a collection of vertices (dots) and edges; by "bipartite" I mean that the dots come in two different types/colors; by "weighted" I mean each edge is labeled with a number.

More specifically, the block matrix obtained from a direct sum corresponds to a disconnected graph. The direct sum of two matrices is obtained by stacking them together into one larger array. (Not unlike the direct sum of vectors.) The result is a big block matrix with zero-blocks. The graph of that matrix is obtained by stacking the graphs of the original matrices together.

The set of equations is thus represented by a single equation. The perfect solution is can be expressed in the same symbols and matrix algebra gives us a routine procedure for locating the solution. Since matrices can be multiplied together according to simple rules, they form an ideal tool for effecting linear transformations. Besides, matrix transformations can be represented within an actual matrix kind of array on the panel.