MATLAB matrix manipulation

Organizing J in a three-dimensional array is elegant, but it does not fit well into the standard routines of MATLAB for matrix manipulation. There is no command for the calculation of the pseudoinverse J+ of such a three-dimensional array. There are several ways around this problem one of them is discussed in the following. The matrices R(k) and R(k + 5k) as well as each matrix < RIdk, are vectorized, i.e., unfolded into long column vectors r(k) and r(k + 5k). The nk vectorized partial derivatives then form the columns of the matricized Jacobian J. The structure of the resulting analogue to Equation 7.13 can be represented graphically in Equation 7.17. 

To understand the concepts of the methods described in the following chapters, one should have an understanding of the basics of linear algebra. This chapter will serve as a short refresher. Linear algebra essentially deals with vector and matrix manipulations, all of which can easily be performed by using the MATLAB software. However, an insight into some of the concepts behind the operations may be helpful. 

MATLAB supports every imaginable way that one can manipulate vectors and matrices. We only need to know a few of them and we will pick up these necessary ones along the way. For now, we ll do a couple of simple operations. With the vector x and matrix a that we ve defined above, we can perform simple operations such as... 

MATLAB offers many tools for matrix operations and manipulations. Table 15.5 shows examples of these capabilities. We will explain MATLAB s matrix operations in more detail in Section 15.5. 

A listing of MATLAB functions for manipulating sparse matrices is returned by the corrunand sparfun. With these sparse functions, the matrix above can be generated more efficiently by the code,... 

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