A PPT

1. Applications of Linear Algebra in
Scientific Fields
• A Study by Harshita Sarma
• Arya Vidyapeeth College (Autonomous)
• 2025

2. Introduction
• - Definition of Linear Algebra
• - Importance in science and technology
• - Explored applications overview

3. History of Linear Algebra
• - Origins in Babylonian and Chinese math
• - Descartes, Leibniz, Gauss contributions
• - 19th-20th century developments

4. Core Concepts
• - Scalars, Vectors
• - Vector operations: addition, dot/cross
product
• - Matrix operations and properties

5. Systems of Linear Equations
• - Definition and structure
• - Matrix representation: AX = B
• - Example equations

6. Solving Linear Systems
• - Augmented matrices
• - Elementary row operations
• - Gaussian elimination example

7. Applications Overview
• - Genetics
• - Cubic spline interpolation
• - Traffic flow
• - Robotics
• - Data transformation
• - Electric circuits

8. Genetics
• - Gene expression matrix
• - Use of PCA, eigenvectors
• - Gene clustering and analysis

9. Cubic Spline Interpolation
• - Smooth curve fitting
• - Tridiagonal matrices
• - Solving spline equations

10. Traffic Flow Analysis
• - Roads modeled as graphs
• - Flow matrices and conservation
• - Solving equilibrium systems

11. Robotics
• - Kinematics and dynamics
• - Transformation matrices
• - Path planning and control systems

12. Data Transformation
• - Scaling and normalization
• - PCA for dimensionality reduction
• - Feature extraction with matrices

13. Electric Circuits
• - Kirchhoff’s and Ohm’s Laws
• - Matrix formulation of circuits
• - Gaussian elimination for current

14. Wheatstone Bridge
• - Precise resistance measurement
• - Balanced bridge matrix equations
• - Example calculation

15. Conclusion
• - Real-world applications of Linear Algebra
• - Cross-disciplinary importance
• - Supports scientific and engineering
innovation