1.3.2. Vectors

To enter vectors use the square brackets and separate the elements with commas or blanks for a row vector, e.g.: v = [-1. , 2., %pi].

In SCILAB, vectors are essentially arrays of numbers. When you want to create a vector, you use square brackets to encapsulate the numbers. Elements within this bracket can be separated by commas or spaces. For example, v = [-1., 2., %pi] creates a vector v containing three elements: -1, 2, and the value of π (pi). This is how you effectively define what is known as a row vector.

Think of a vector as a row of seats in a theater. Each seat can be occupied by a number representing a ticket holder. Just as you can have empty seats or different ticket holders in the same row, you can create vectors with various numbers.

The transpose of a vector (or matrix) is expressed using the apostrophe, for example, type: v'.

Transposing is a common operation in mathematics and programming. For a vector, transposing means converting a row vector into a column vector. In SCILAB, this can be easily done using the apostrophe ('). For example, if v is a row vector, typing v' will give you the corresponding column vector.

Imagine a classroom where students are sitting in rows. If you wanted to turn that layout into a list of students standing in a line, you would simply 'transpose' the seating arrangement, moving each student from their row into a single line.

To enter a column vector, use any of the following procedures: w = [3; -2; 5], or r = [6 <return> -2 <return> 10].

Column vectors in SCILAB can be created similarly to row vectors but with vertical separation. Elements can either be separated by semicolons or entered line by line. For example, w = [3; -2; 5] creates a column vector with three elements: 3, -2, and 5. This is quite useful for representing data in a vertical format, like a list of ingredients required for a recipe.

Think of a column vector like a shopping list that's written vertically down a piece of paper. Each item you need is listed one underneath the other, making it clear and organized.

You can create a row vector by indicating a starting value, an increment (or decrement), and an ending value, all separated by the colon (:) operator as follows: vector_name=starting_value:increment:ending_value, for example, x=-10.0:0.5:10.0.

In SCILAB, you can quickly create sequences of numbers using the colon operator. For instance, if you want to create a vector that starts at -10.0, increases by 0.5, and ends at 10.0, you can simply type x = -10.0:0.5:10.0. This saves time compared to entering each number individually.

Imagine a countdown where you start from a high number and move downwards in regular intervals—like counting down from 10 to 1 in steps of 1. You can easily create a list of all the numbers using a simple phrase like ‘count down from 10 by 1’.

Let's apply a function to the vector x, try: y = sin(x*%pi/10).

You can apply mathematical functions to entire vectors in SCILAB at once. For instance, if x is a vector of values, using y = sin(x*%pi/10) calculates the sine of each element in x, effectively creating a new vector y that stores the results. This feature allows for efficient computations without needing to loop through each individual element.

Think of this as a factory line where you place raw materials (the elements of vector x) and you perform the same operation on every item at once (finding the sine of each number), producing finished products (the new vector y) quickly without inspecting each item separately.

We can plot the vectors x and y using: plot(x,y,'x','y','first plot').

SCILAB allows you to visualize data by plotting it on graphs. The command plot(x,y,'x','y','first plot') creates a plot where the x-axis takes values from vector x and the y-axis takes values from vector y. This way, you can see the relationship between the two sets of data graphically.

Imagine you're trying to show your friend how your height changes over the years. Instead of just telling them the numbers, you draw a chart that depicts this change visually, making it easier for them to grasp the trend and understand your growth over time.

To extract elements of the vectors, try: u(3), u(2) + v(1).

SCILAB allows you to access individual elements in a vector using indexing. For example, u(3) retrieves the third element of vector u, while u(2) + v(1) sums the second element of u with the first element of v. This feature is particularly useful for manipulating data stored in vectors, as it allows you to work on specific elements easily.

Consider a bookshelf where each book represents an element in a vector. If you want to grab the third book on that shelf, you simply refer to it by its position number. Next, if you want to summarize information about the second book and the first book from another shelf, you can easily pull them together and make a note of their content.

Vectors can also contain characters as their elements, e.g., letters = ['a', 'b', 'c', 'd'].

In SCILAB, it's also possible to create vectors that contain characters, known as string vectors. For example, letters = ['a', 'b', 'c', 'd'] creates a vector where each element is a character. This is particularly useful when you're working with data that involves text, like names or labels.

Think of this like a list of names in a phone book. Each name can be thought of as an element in the vector. You can use these elements later to find contact details based on their given characters, just like you would when searching through a list of friends.

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