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Linear Algebra

Linear algebra has been a crucial part of my learning journey, especially as I ventured into quantum computing. I started with Gilbert Strang's Introduction to Linear Algebra to build a strong foundation, but I often found myself exploring much deeper concepts and proofs beyond what the book covered. Throughout this process, Mathematics Stack Exchange became an invaluable resource for clarifying doubts, solving challenging problems, and learning through engaging discussions with the community.

These notes are an attempt to organize and share what I’ve learned over the years. They reflect not only the material from Strang's book but also the extended explorations and insights I’ve gained while tackling questions and problems. In addition to core linear algebra topics, I have ventured into related areas such as Fourier series, orthogonal polynomials (Legendre, Hermite, Chebyshev), and special functions. Having enrolled in Math 6108 Applied Matrix Theory at Missouri S&T, my notes extend well beyond the typical scope of a 6000-level advanced graduate course.

Book 1: Introduction to Vectors
Book 2: Markov Process - Subspaces
Book 3: Subspaces Continue
Book 4: Intersection, Union, and Sum
Book 5: Orthogonality
Book 6: Orthogonality Continue
Book 7: Eigenvalues and Eigenvectors
Book 8: Differential Equations Continue
Book 9: Singular Value Decomposition
Book 10: SVD Continue
Book 11: Linear Transformation
Book 12: Fourier Series, Transform and Delta Function
Book 13: Legendre and Hermite
Book 14: Laguerre, Bessel and Chebyshev
Book 15: Complex Vectors - Cryptography
Book 16: Encryption - Probability
Book 17: Probability and Statistics Continue
Miscellaneous 1: Linear Algebra