2.5.1. Entering a vector

A vector is a special case of a matrix. The purpose of this section is to show how to create vectors and matrices in MATLAB. As discussed earlier, an array of dimension 1×n is called a row vector, whereas an array of dimension m×1 is called a column vector.

In MATLAB, vectors are considered as a specific type of matrix. A vector can be either a row vector or a column vector. A row vector has one row and multiple columns, while a column vector has multiple rows and just one column. This distinction is crucial as it determines how we work with and manipulate the data.

Think of a row vector as a single row of seats in a theater, where each seat represents an element of the vector. A column vector, on the other hand, is like a single column of those seats, where each seat also represents an element. Just as you can have multiple rows and columns in a theater layout, you can have various vectors in MATLAB.

The elements of vectors in MATLAB are enclosed by square brackets and are separated by spaces or by commas. For example, to enter a row vector, v, type

v = [1 4 7 10 13] v = 1 4 7 10 13

To create a row vector in MATLAB, you must encapsulate the elements within square brackets. Each element can be separated by spaces or commas, allowing you to list the values you want to include in the vector. When you enter the command, MATLAB outputs the same vector format, confirming it has been successfully created.

Imagine writing down your grocery list on a piece of paper. Each item is like an element in your row vector, and you can separate them with commas or just spaces. This is how you create a list of numbers in MATLAB—similar to making a list of your groceries!

Column vectors are created in a similar way, however, semicolon (;) must separate the components of a column vector,

w = [1;4;7;10;13] w = 1 4 7 10 13

When creating a column vector, you still use the square brackets for enclosing the elements, but the components must be separated by semicolons. This indicates to MATLAB that you are moving to a new row for each new value. The output displayed will show the elements listed vertically, aligning with the nature of column vectors.

Think of a column vector like a list of names on a job application, where each name is stacked one below the other. You could use a comma to separate names on a horizontal application, but for a column format, you would list them one after another, just as you do in MATLAB.

On the other hand, a row vector is converted to a column vector using the transpose operator. The transpose operation is denoted by an apostrophe or a single quote (').

w = v' w = 1 4 7 10 13

Transposing a vector in MATLAB changes its orientation. If you start with a row vector and apply the transpose operator (denoted by '), MATLAB switches it to a column vector. This operation is essential in linear algebra and matrix computations as it allows for conversion between the two types of vectors.

Think of transposing like flipping a page in a book. When you flip a book from a horizontal orientation to vertical, the text reorients accordingly. In the same way, transposing a vector changes the way it's represented, switching from a row format to a column format.

Thus, v(1) is the first element of vector v, v(2) its second element, and so forth. Furthermore, to access blocks of elements, we use MATLAB’s colon notation (:). For example, to access the first three elements of v, we write,

v(1:3) ans = 1 4 7

In MATLAB, you can access specific elements of a vector using indexing. Each element can be accessed by its position in the vector, starting from 1. The colon operator (:) allows you to specify a range of indices, letting you retrieve multiple elements at once. For instance, v(1:3) accesses the first three elements simultaneously.

Imagine a bookshelf where each book represents an item in your vector. If you wanted to read the first three books, you would simply go to the first three slots on the shelf. In MATLAB, using the colon operator allows you to quickly access a range of 'books' from your 'shelf' of data.

Or, all elements from the third through the last elements,

v(3,end) ans = 7 10 13 where end signifies the last element in the vector.

The keyword 'end' in MATLAB is a convenient way to access the last element of a vector. When you want elements from a specific position to the end of the vector, you can use 'end' in your indexing. For example, v(3,end) retrieves elements starting from the third position through to the last element.

Think of opening a candy jar where the last few candies are at the bottom. If you're told to grab everything from the third candy to the last, you'd simply reach in and take all the remaining candies. In MATLAB, 'end' allows you to easily reference that last candy without needing to count how many you have.

If v is a vector, writing

v(:) produces a column vector, whereas writing v(1:end) produces a row vector.

In MATLAB, using v(:) is an efficient way to convert any vector into a column format regardless of its initial orientation. Conversely, v(1:end) is a method that retrieves all elements, maintaining the original row vector format. This flexibility is valuable for operations that require a specific arrangement of data.

Think of a toolbox where you can rearrange your tools as you see fit. Some tasks require tools to be stacked in a tray (column), while others need them laying flat (row). In MATLAB, switching between orientations allows you to organize your 'tools' of data in the way that's best suited for your task!

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