By Claus Fuher

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**Additional info for Computing With Python: An Introduction to Python for Science & Engineering**

**Example text**

Like which are slight variants of the above. For instance, zeros_like (A) is equivalent to zeros (shape (A)). ] , [ 0. , 1. ] , [ 0. , Accessing and Changing the Shape The number of dimensions is what distinguishes a vector from a matrix. The shape is what distinguishes vectors of different sizes, or matrix of different sizes. In this section we examine how to obtain and change the shape of an array. 1 The shape function The shape of a matrix is the tuple of its dimensions. The shape of an n x m matrix is the tuple (n,m).

4, so we only provide some illustrating examples here. ]) M[0,0] M[l:] M[1] # 1. ]) Chapter V Linear Algebra: Arrays # access v[0] # 1. ]) # error! Linear Algebra Operations The essential operator that performs most of the usual operations of linear algebra is the Python function dot. 3 for more details): dot(M,y) # matrix vector multiplication; returns a vector It may be used to compute a scalar product between two vectors dot(v,w) # scalar product; the result is a scalar Finally, it is used to compute the matrix-matrix product dot(M,N) # results in a matrix Solving a Linear System If ,4 is a matrix and b is a vector you solve the linear equation Ax = b using solve which has the syntax x = solve (A, b).

In the first two lines they only differ in the way they are displayed. The real difference in accuracy is between a and its single precision counterpart a2. max # 1. 3 Complex Numbers Complex numbers are an extension of the real numbers frequently used in many scientific and engineering fields. Complex Numbers in Mathematics Complex numbers consist of two floating point numbers, the real part a of the number and its imaginary part b. In mathematics a complex number is written as 2 = « + M, where i defined by i2 = -1 is the imaginary unit.