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- 1.
Applications of LinearAlgebra in
Scientific Fields
• A Study by Harshita Sarma
• Arya Vidyapeeth College (Autonomous)
• 2025
- 2.
- 3.
History of LinearAlgebra
• - 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 LinearEquations
• - Definition and structure
• - Matrix representation: AX = B
• - Example equations
- 6.
- 7.
Applications Overview
• -Genetics
• - Cubic spline interpolation
• - Traffic flow
• - Robotics
• - Data transformation
• - Electric circuits
- 8.
Genetics
• - Geneexpression matrix
• - Use of PCA, eigenvectors
• - Gene clustering and analysis
- 9.
- 10.
Traffic Flow Analysis
•- Roads modeled as graphs
• - Flow matrices and conservation
• - Solving equilibrium systems
- 11.
- 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-worldapplications of Linear Algebra
• - Cross-disciplinary importance
• - Supports scientific and engineering
innovation