Matrix Exponentiation | n Degree Linear Recurrence | Super Detailed | codestorywithMIK

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Published on May 14, 2025 3:05:42 PM ● Video Link: https://www.youtube.com/watch?v=gX8KaRlkoN0

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Binary Exponentiation | Fast Exponentiation -    • Binary Exponentiation | Fast Exponentiatio...  

This is the 5th video of our playlist "Maths Concepts & Questions". Find the Details below:

Video Name: Matrix Exponentiation | n Degree Linear Recurrence | Detailed | codestorywithMIK
Video #: 5

🔍 Mastering Maths for Coding: Simplified & Powerful.

🎥 Welcome to the 5th Video of my Maths Concepts Playlist!
🚀 In this important session, we’ll dive deep into Matrix Exponentiation | n Degree Linear Recurrence | Detailed | codestorywithMIK

Github Code Link (C++ and Java) - https://github.com/MAZHARMIK/Interview_DS_Algo/blob/master/Mathematical/Matrix Exponentiation.cpp

🔍 What's Inside?

Then this video is exactly for you!

In this session, we’ll explore Matrix Exponentiation — a powerful technique to solve recurrence relations in logarithmic time!

We’ll cover:


✅ What is Matrix Exponentiation and why it's useful in DSA

✅ Understand the concept through the Fibonacci example

✅ Step-by-step derivation and proof to build the transformation (T) matrix

✅ What is a Linear Recurrence Relation and how to identify its Degree

✅ Complete C++ Code for Matrix Exponentiation

✅ Neat Matrix Multiplication Code used for transformations

✅ Full time complexity analysis


👨 ‍🏫 Explained with beginner-friendly language, math intuition, and no shortcuts!

👩 ‍💻 Who Should Watch?
Anyone preparing for coding interviews, DSA practice, or competitive programming problems involving recurrence relations. Matrix exponentiation is a must-know trick when brute-force fails!

🚀 Let’s level up your math arsenal and make your DSA code blazing fast 🔥

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🧠 Summary:
In this video, I explain how Matrix Exponentiation in detail. We will understand it with a simple example of Fibonacci Sequence which has a linear recurrence relation and we will also understand about degree of a recurrence relation. In the end we understand how easily we can write Matrix Exponentiation and Matrix Multiplication code.


✨ Timelines ✨
00:00 - Introduction
0:28 - Motivation
1:07 - What and Why do we need Matrix Exponentiation?
1:30 - Understanding Linear Recurrence using Fibonacci
04:00 - How ?? Matrix Representation of Fibonacci
6:49 - Finding T matrix with Proof
13:35 - Important Example with n = 2 and n = 3
19:53 - Generic Formula for F(n)
21:27 - Degree of a Recurrence Relation
24:24 - Recurrence relation having degree 3 example
26:24 - Exponentiation ? Fibonacci number in log(n)
28:52 - Binary Exponentiation to Matrix Exponentiation code
36:03 - Matrix Multiplication code
44:52 - Time Complexity log(n)


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