📐 Linear Algebra

Last Updated: Jan 2026

Linear Algebra is the branch of mathematics used to work with:

  • Vectors
  • Matrices
  • Linear transformations

🗣 Hinglish Tip: Linear algebra = data ko arrays + math rules ke saath samajhna

Linear Algebra (Roadmap)

In programming-focused linear algebra, we mainly cover:

  • Vectors
  • Matrices
  • Matrix Operations
  • Linear Transformations

Vector

A vector is an ordered collection of numbers.

Example:

[2, 4, 6]

In programming:

  • A vector is usually an array
  • Each value represents a feature or dimension

🗣 Hinglish Tip: Vector ko array samjho jo direction + value dono batata hai

Matrix

A matrix is a collection of vectors arranged in rows and columns.

Example:

[ 1  2  3 ]
[ 4  5  6 ]

In programming:

  • A matrix is a 2D array
  • Used to store datasets, images, weights

🗣 Hinglish Tip: Matrix = multiple vectors ko table form me rakhna

Matrix Operations

Common operations used in code:

  • Addition
  • Subtraction
  • Multiplication
  • Transpose

These operations allow:

  • Combining data
  • Scaling values
  • Transforming structures

Linear Transformation

A linear transformation changes data while:

  • Preserving straight lines
  • Maintaining proportional relationships

In programming, it is used to:

  • Rotate images
  • Scale data
  • Transform feature space in ML

Example idea:

Input Vector → Matrix → Output Vector

🗣 Hinglish Tip: Linear transformation = data ko rule ke according badalna

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