Basic Complex and Matrix Operations 1.2 2006/08/03 16:41:47 GMT-5 2006/08/21 13:30:41.300 GMT-5 Darryl Morrell morrell@asu.edu Darryl Morrell morrell@asu.edu Complex operations LabVIEW MathScript MATLAB Matrix operations Octave This module covers basic complex and matrix operations in an m-file environment.

Complex numbers m-file environments have excellent support for complex numbers. The imaginary unit is denoted by i or (as preferred in Electrical Engineering) j. To create complex variables z1 7 and z2 2 e simply enter z1 = 7 + j and z2 = 2*exp(j*pi) The table gives an overview of the basic functions for manipulating complex numbers, where z is a complex number. Manipulating complex numbers m-file Re(z) real(z) Im(z) imag(z) z abs(z) Angle(z) angle(z) z* conj(z)

Operations on Matrices In addition to scalars, m-file environments can operate on matrices. Some common matrix operations are shown in the Table below; in this table, M and N are matrices. Common matrix operations Operation m-file MN M*N M-1 inv(M) MT M' det(M) det(M) Some useful facts: The functions length and size are used to find the dimensions of vectors and matrices, respectively. Operations can also be performed on each element of a vector or matrix by proceeding the operator by ".", e.g .*, .^ and ./. Let A 1 1 1 1 . Then A^2 will return AA 2 2 2 2 , while A.^2 will return 12 12 12 12 1 1 1 1 . Given a vector x, compute a vector y having elements yn 1 xn . This can be easily be done the command y=1./sin(x) Note that using / in place of ./ would result in the (common) error "Matrix dimensions must agree".