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Gate Data Science and AI
·
Module 2
Mathematical Foundations: Linear Algebra
1
Vector Operations: Dot, Cross, and Projections
Apply vector operations including dot product, cross product, and projections.
2
Matrix Operations: Manual and NumPy
Perform matrix operations (addition, multiplication) both manually and using NumPy.
3
Gaussian Elimination for Solving Linear Systems
Solve systems of linear equations using Gaussian elimination.
4
Determinants and Matrix Inverses
Compute the determinant and inverse of a square matrix.
5
Matrix Rank Using Row Reduction
Determine the rank of a matrix using row reduction techniques.
6
Eigenvalues and Eigenvectors: Calculation and Application
Define eigenvalues and eigenvectors and solve for them in 2x2 and 3x3 matrices.
7
Matrix Decomposition with SVD
Apply Singular Value Decomposition (SVD) to decompose a matrix.
8
Matrix Operations with NumPy
Use NumPy to compute determinants, inverses, eigenvalues, and SVD of matrices.
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Python for Data Science: Foundations
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Mathematical Foundations: Calculus for Optimization