【Fundamentals】MATLAB Vectors and Matrix Variables, Elements, Initialization, Identification, and Extraction

# 2.1.1 Creation and Initialization of Vector Variables

In MATLAB, vector variables are one-dimensional arrays used to store elements of the same data type. The syntax for creating a vector variable is as follows:

vector_name = [element1, element2, ..., elementN];

For example, to create a vector variable containing the numbers 1, 2, 3, 4, 5:

my_vector = [1, 2, 3, 4, 5];

After creating a vector variable, you can use the `disp` function to view its contents:

disp(my_vector)

Output:

1      2      3      4      5

# 2. Vectors and Matrices in MATLAB

## 2.1 Vector Variables

### 2.1.1 Creation and Initialization of Vector Variables

**Creating Vector Variables**

In MATLAB, vector variables can be created using square brackets `[]`, and vector elements are specified within these brackets. For example:

>> v = [1, 3, 5, 7, 9];

**Initializing Vector Variables**

Vector variables can also be initialized using `zeros()`, `ones()`, or `rand()` functions.

* `zeros(n)`: Creates a vector with `n` elements, all of which are set to 0.
* `ones(n)`: Creates a vector with `n` elements, all of which are set to 1.
* `rand(n)`: Creates a vector with `n` elements, whose values are randomly distributed between 0 and 1.

For instance:

>> v = zeros(1, 5);   % Creates a vector with 5 elements, all set to 0
>> v = ones(1, 5);    % Creates a vector with 5 elements, all set to 1
>> v = rand(1, 5);    % Creates a vector with 5 elements, values randomly between 0 and 1

#### 2.1.2 Accessing and Modifying Vector Elements

**Accessing Elements**

Vector elements are accessed using subscripts. Subscripts start from 1, indicating the position of the element in the vector. For example:

>> v = [1, 3, 5, 7, 9];
>> v(3)   % Accesses the third element in the vector
ans = 5

**Modifying Elements**

Vector elements are modified by assigning new values using subscripts. For example:

>> v = [1, 3, 5, 7, 9];
>> v(3) = 4;   % Modifies the third element in the vector
>> v
ans = [1, 3, 4, 7, 9]

## 2.2 Matrix Variables

### 2.2.1 Creation and Initialization of Matrix Variables

**Creating Matrix Variables**

In MATLAB, matrix variables can be created using square brackets `[]`, and matrix elements are specified within these brackets, with elements separated by semicolons. For example:

>> A = [1, 3, 5; 2, 4, 6; 7, 8, 9];

**Initializing Matrix Variables**

Matrix variables can also be initialized using `zeros()`, `ones()`, or `rand()` functions.

* `zeros(m, n)`: Creates a matrix with `m` rows and `n` columns, all of which are set to 0.
* `ones(m, n)`: Creates a matrix with `m` rows and `n` columns, all of which are set to 1.
* `rand(m, n)`: Creates a matrix with `m` rows and `n` columns, whose values are randomly distributed between 0 and 1.

For instance:

>> A = zeros(3, 3);   % Creates a 3x3 matrix with all elements set to 0
>> A = ones(3, 3);    % Creates a 3x3 matrix with all elements set to 1
>> A = rand(3, 3);    % Creates a 3x3 matrix with values randomly between 0 and 1

#### 2.2.2 Accessing and Modifying Matrix Elements

**Accessing Elements**

Matrix elements are accessed using subscripts. Subscripts start from 1, indicating the row and column positions of the element in the matrix. For example:

>> A = [1, 3, 5; 2, 4, 6; 7, 8, 9];
>> A(2, 3)   % Accesses the element in the second row and third column
ans = 6

**Modifying Elements**

Matrix elements are modified by assigning new values using subscripts. For example:

>> A = [1, 3, 5; 2, 4, 6; 7, 8, 9];
>> A(2, 3) = 7;   % Modifies the element in the second row and third column
>> A
ans = [1, 3, 5; 2, 4, 7; 7, 8, 9]

# 3. MATLAB Variable Identification and Extraction

## 3.1 Variable Identification

### 3.1.1 Rules for Naming Variables

Variable names in MATLAB follow these rules:

- Must start with a letter, followed by letters, numbers, or underscores.
- Cannot contain spaces or special characters (e.g., $, #, %).
- Cannot be the same as MATLAB reserved words (e.g., for, if, else).
- It is recommended to use descriptive names for clarity on the variable's purpose.

### 3.1.2 Variable Scope and Lifetime

The scope and lifetime of variables in MATLAB are determined by where they are defined.

- **Global variables:** Defined at the top of a script or function file. They are visible throughout the file.
- **Local variables:** Defined within a function or subfunction. They are only visible within that function or subfunction.
- **Lifetime:** The lifetime of a variable begins when it is created and ends when the script or function execution concludes.

## 3.2 Variable Extraction

### 3.2.1 Reading Variable Values

The `disp()` function or typing the variable name directly in the command line can be used to read variable values.

% Creating a variable
x = 10;

% Using disp() to read variable value
disp(x)   % Output: 10

% Typing the variable name directly to read its value
x   % Output: 10

### 3.2.2 Assigning Variable Values

The assignment operator `=` can be used to assign values to variables.

% Creating a variable and assigning a value
x = 10;

% Reassigning the variable
x = 20;

% Reading the variable value
disp(x)   % Output: 20

### 3.2.3 Type Conversion of Variables

MATLAB allows converting variables from one type to another. The `cast()` function or direct type conversion operators (e.g., `int32()`, `double()`) can be used.

% Creating a double type variable
x = 10.5;

% Converting x to int32 type
y = int32(x);

% Reading the variable value
disp(y)   % Output: 10

# 4. Operations on Vectors and Matrices in MATLAB

## 4.1 Operations on Vector Variab