Vectors in MATLAB

Definition:

Vector means a 1D array of numbers.

It can be of two types:

  • Row Vector → Numbers are arranged in a row.
  • Column Vector → Numbers are arranged in a column

Examples:

% Row vector
v1 = [1 2 3 4];
% Column vector
v2 = [1; 2; 3; 4];
% Range with step
v3 = 0:0.5:2;        % [0 0.5 1.0 1.5 2.0]
% Linearly spaced
v4 = linspace(0, 1, 5);   % [0 0.25 0.5 0.75 1]

Vector Operations:

So here many operations can be easily performed with these vectors in MATLAB.

1. Addition & Subtraction

In this type of vector operation both vectors should be of the same size.

A = [1 2 3];
B = [4 5 6];
C = A + B   % [5 7 9]
D = A - B   % [-3 -3 -3]

Output

C = 1×3

     5     7     9

D = 1×3

    -3    -3    -3

2. Scalar Multiplication

In this scalar multiplication you, all can multiply each element of a vector by a number (scalar).

A = [1 2 3];
k = 2;
C = k * A   % [2 4 6]

Output

C = 1×3

     2     4     6

3. Dot Product (Inner Product)

Here we can follow Row × Column method and at the end we will get a single number (scalar) result.

A = [1 2 3];
B = [4 5 6];
dotProd = dot(A,B)   % 1*4 + 2*5 + 3*6 = 32

Output

dotProd = 32

4. Cross Product

So, this basically only applies to 3d vectors and the result is a new vector.

A = [1 2 3];
B = [4 5 6];
crossProd = cross(A,B)   % [-3 6 -3]

Output

crossProd = 1×3

    -3     6    -3

5. Element-wise Operations

In element-wise operations it is applied to each element (called .*, ./, .^).

A = [1 2 3];
B = [4 5 6];
C = A .* B   % [4 10 18] (element-wise multiplication)
D = A .^ 2   % [1 4 9]   (square of each element)

Output

C = 1×3

     4    10    18

D = 1×3

     1     4     9

Matrices in MATLAB

Definition:

So, a matrix is a 2D array of numbers arranged in rows × columns.

Examples:

% Matrix creation
A = [1 2 3; 4 5 6]   % 2×3 matrix

Output

A = 2×3

     1     2     3

     4     5     6

% Access elements
val = A(2, 3)        % Second row, third column → 6

Output

val = 6

% Modify element
A(1, 1) = 10

Output

A = 2×3

    10     2     3

     4     5     6

% Matrix size
[r, c] = size(A)     % r = 2, c = 3

Output

r = 2

c = 3

Matrix Operations

% Define matrix A (2x3)
A = [1 2 3; 
     4 5 6];
% Define matrix B (2x3)
B = [1 1 1; 
     1 1 1];
% Matrix addition (both are 2x3)
C = A + B;
% Matrix multiplication (2x3 * 3x2 → 2x2)
D = A * B';
% Element-wise multiplication (2x3 .* 2x3 → 2x3)
E = A .* B;
% Transpose of A (2x3 → 3x2)
A_T = A';

Data Types in MATLAB

So, as we know that it is a dynamically typed language, which means that you don’t have to explicitly declare the type of a variable.

a = 10;        % integer
b = 3.14;      % double
c = 'Hello';   % string

Common Data Types

But, in automotive applications (ECU modelling, CAN parsing, signal processing) specific data types are very important:

  • int8, uint8, int16, uint16 → for ECU I/O signals (memory optimized).
  • single, double → For control algorithms and mathematical models.
  • Boolean → ON/OFF or TRUE/FALSE signals (e.g., ignition switch, ABS flag).
  • fixed-point (via Fixed-Point Toolbox) → Hardware-level implementation when floating-point is not supported.

Example (CAN Parsing)

speed = uint16(150);      % Vehicle speed signal (0–65535 range)
ignition = boolean(1);    % Ignition ON
torque = int16(-120);     % Engine torque (signed value)

These data types ensure that Simulink models and expressions communicate efficiently and efficiently.

Useful MATLAB Functions

v = [1 2 3];
M = [1 2; 3 4; 5 6];
x = 10;
A = [0 1 0];

Commonly Used Functions

length(v) → length of vector (no. of elements).

length(v)     % Output: 3

size(M) → indicates the rows and columns of the matrix.

size(M)       % Output: 3   2

class(x) → Checks the data type of the variable.

class(x)      % Output: ‘double’

isnumeric(x) → Checks whether the variable is numeric or not.

isnumeric(x)  % Output: 1 (true)

logical(A) → Converts values ​​to boolean (true/false).

logical(A)    % Output: [0 1 0] → false true false

These functions are very useful in basic debugging and data handling, especially when you work with signals and matrices in automotive Simulink/MATLAB.

Vectorization vs Looping

The biggest advantage of MATLAB is that it is optimized for vectorized operations.

Which means you do not need to write a for loop every time. Performing direct operations on a vector/matrix is ​​faster and cleaner.

Example 1: Using Loop

A = [1 2 3 4 5];
for i = 1:length(A)
    B(i) = A(i) ^ 2;
end
% Output: B = [1 4 9 16 25]

Example 2: Vectorized Way

A = [1 2 3 4 5];
B = A .^ 2;     % Direct element-wise square
% Output: B = [1 4 9 16 25]

Why Vectorization is Better?

  • Speed: MATLAB is internally optimized for matrix/vector operations.
  • Cleaner Code: The work is done in one line.
  • Scalable: Efficient for large data sets and automotive signals.

Automotive Use Cases