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Coding the Matrix: Linear Algebra through Applications to by Philip N. Klein

By Philip N. Klein

An enticing creation to vectors and matrices and the algorithms that function on them, meant for the coed who understands the best way to application. Mathematical thoughts and computational difficulties are inspired via functions in laptop technology. The reader learns by means of doing, writing courses to enforce the mathematical strategies and utilizing them to hold out initiatives and discover the purposes. Examples contain: error-correcting codes, adjustments in photographs, face detection, encryption and secret-sharing, integer factoring, removal viewpoint from a picture, PageRank (Google's rating algorithm), and melanoma detection from telephone good points. A significant other internet site,
provides information and help code. many of the assignments should be auto-graded on-line. Over 200 illustrations, together with a range of proper xkcd comics.

Chapters: The functionality, the sphere, The Vector, The Vector area, The Matrix, the root, size, Gaussian removing, the internal Product, exact Bases, The Singular worth Decomposition, The Eigenvector, The Linear software

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Len(L) − 1, maps i to L[i] You can write this procedure from scratch or write it in terms of list2dict(L, keylist). Use the statement >>> reload(dictutil) to reload your module, and then test listrange2dict on the list ['A','B','C']. 3 Loops and conditional statements Comprehensions are not the only way to loop over elements of a set, list, dictionary, tuple, range, or zip. For the traditionalist programmer, there are for-loops: for x in {1,2,3}: print( In this statement, the variable x is bound to each of the elements of the set in turn, and the statement print(x) is executed in the context of that binding.

This would result in an error message if some element of listoflists were not a two-element list. Mutating a list: indexing on the left-hand side of = You can mutate a list, replacing its ith element, using indexing on the left-hand side of the =, analogous to an assignment statement: CHAPTER 0. THE FUNCTION 33 >>> mylist = [30, 20, 10] >>> mylist[1] = 0 >>> mylist [30, 0, 10] Slices can also be used on the left-hand side but we will not use this. 6 Tuples Like a list, a tuple is an ordered sequence of elements.

4 (Page 13). What is the probability distribution of the output? Because f is an invertible function, there is one and only one input for which the output is 0, namely A. Thus the probability of the output being 0 is exactly the same as the probability of the input being A, namely 9/95.. Similarly, for each of the integers 0 through 25 comprising the co-domain of f , there is exactly one letter that maps to that integer, so the probability of that integer equals the probability of that letter. } The previous example illustrates that, if the function is invertible, the probabilities are preserved: the probabilities of the various outputs match the probabilities of the inputs.

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