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Scalars are quantities that are invariant under coordinate transformation (eg, mass); Vectors are sets of quantities which if organized as v = [v1 , v2 , v3 ] transform between coordinate frames according to vb = Rb va where Rb is a rotation matrix and a a the superscript on v indicates the frame in which it is represented This strict de nition of vectors is required to distinguish which items arranged as [a, b, c] can be transformed between coordinate systems via vector transformation operations (ie, rotations) Some quantities although convenient to organize in a vector-like notation, are not vectors in this strict sense In this strict sense, Euler angle 3-tuple ( , , ) and its derivative d , d , d are not vectors Note for example that each element of dt dt dt the Euler angle derivative 3-tuple is de ned in a di erent reference frame

unshift @ARGV,qw/-v --/ if (@ARGV == 0);

Refer back to 2 if you want more information on the manipulation of arrays If you want to process command line arguments, rather than doing it yourself, the best method is to use either the standard or extended options supported by the Getopt::Std and Getopt::Long modules, respectively Both Getopt::Std and Getopt::Long support functions that process the individual elements of the @ARGV array looking for command line options When the function finds a valid argument, it removes it from the array Any elements of the @ARGV array that cannot be identified as options remain in the @ARGV array, so you can continue to use the values supplied in your script

The Getopt::Std module provides a very simple interface for extracting options from the command line arguments Each option can only be specified with a single letter, for example:

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this rule will be violated is when, in the middle of text, considerable space would be wasted by writing out the column vector

Partial Class Home Inherits System.Web.UI.Page Protected Sub Page_Load(ByVal sender As Object, _ ByVal e As System.EventArgs) Handles Me.Load Me.Master.PageSubTitle.Text = "Home" ' control the visibility of sections restricted to specific roles pnlManager.Visible = User.IsInRole("Manager") pnlEmployee.Visible = User.IsInRole("Employee") End Sub End Class

There are two functions, getopt and getopts:

use Getopt::Std; getopt('ol'); getopts('ol:');

The transpose operation, which is indicated by a superscript , simply exchanges the rows and columns of a matrix Therefore, for B = [bi,j ] Rn m , B = [bj,i ] Rm n Two examples may clarify this operation First, 020 171 000 A = 000 314 200 000 is a matrix in R3 2 Second, for v = 200 , 714 v = 000 200 714

Both functions require a single argument that specifies the list of single-letter arguments you would like to identify on the command line In the case of the getopt function, it assumes that all arguments expect an additional piece of information, such that the example above would accept the following line:

However, it would incorrectly assume that -l was the data for the -o option With the getopts function, each character is taken to be a Boolean value If you want to accept arguments with additional information, then append a colon This means that the preceding script fragment will accept

correctly identifying the -l as a simple switch The getopts function supports combined options For example,

is a matrix in R1 3 which is often referred to as a row vector When a matrix is symmetric, it is straightforward to show that A = A When a matrix is skew-symmetric, A = A The addition of matrices is straightforward and is de ned componentwise When we say that C = A + B for A, B, C Rn m we mean that ci,j = ai,j + bi,j for i [1, n] and j [1, m] In order to add two matrices, their dimensions must be identical Therefore, with the matrices given previously A and v cannot be added If we de ne 100 171 B = 003 200 014 214 then A and B cannot be added or subtracted, but 120 000 A + B = 003 200 300 414 Subtraction of matrices is de ned similarly The symmetric part of a square matrix A is de ned by As = 1 A+A 2 1 A A 2 (B1)

which would correctly be recognized as four individual options, setting the values of $opt_e, $opt_a, $opt_f, and $opt_l to 1 Both getopt and getopts create new variables starting with a prefix of $opt_ The preceding script would create two variables: $opt_o will have a value of 1, and $opt_l will have a value of fileinput If a letter defined to the function is not found, then no variable will be created In addition, for either function, you can also supply a second argument, which should be a reference to a hash:

getopts('i:',\%opts);

The anti-symmetric part of A is de ned by Aa = (B2)

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