Send mail if you have questions about using the book for a university course.

Here is a revised and expanded index for Edition 0.

Here are examples of applications addressed in Coding the Matrix.









crossfade



A line segment between points is given by the convex combinations of those points; if the "points" are images, the line segment is a simple morph between the images.



Perspective rectification



Given a photo of a whiteboard taken at an angle, synthesize a perspective-free view of the whiteboard.









The same transformation can be used in using a Wiimote to make a low-cost interactive whiteboard or light pen (due to Johnny Chung Lee).



Error-correcting codes







Error-correcting codes are used, e.g., by cellphones to preserve data transmitted over a noisy channel while maintaining high throughput.



Integer factorization



522253825433285668885771662040104167 = 891428822186035241∙585861498344390287





Factoring an integer is a hard computational problem (and the RSA cryptosystem depends on it being hard). At the core of the most sophisticated integer-factoring algorithms is a simple problem in linear algebra.

Image blurring



Blurring an image is a simple linear transformation.



Searching within an audio clip



Searching for one audio clip within another can be formulated as a convolution. A convolution can be computed very quickly using the Fast Fourier Transform.



Searching within an image







Convolution can also be done in two dimensions, enabling one to quickly search for a subimage within an image.



Audio and image compression



Compression of audio and images aids efficient storage and transmission. Lossy compression techniques such as those used in MP3 (audio) and JPEG (images) are based in part on linear algebra,

e.g. wavelet transform and Fourier transform.

100% original size 40% original size 10% original size

Face detection



A "classical" approach to face detection is eigenfaces, a technique related to principal component analysis.



2d graphics transformations



Simple transformations that arise in graphics such as rotation, translation, and scaling can be expressed using matrices.



Lights Out



Lights Out is a puzzle in which you must select the correct buttons to push in order for all the lights to go out. Finding a solution can be expressed as a problem in linear algebra.



Minimum-weight spanning forest



Finding the minimum-weight spanning tree of a graph can be interpreted as the problem of finding a minimum-weight basis for a vector space

derived from the graph.

