Algebra
M Linear Algebra
Vectors, matrices, and the geometry of high-dimensional space — the language of machine learning and modern data science.
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Matrices
Rectangular arrays of numbers that encode systems of equations, transformations, and data — the central objects of linear algebra.
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Determinants
A scalar associated with a square matrix measuring the signed volume scaling factor of the linear transformation it encodes.
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Eigenvalues and Eigenvectors
The special directions a linear transformation merely scales — central to PCA, differential equations, and Google's PageRank.
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Principal Component Analysis
Finding the directions of maximum variance in data by computing eigenvectors of the covariance matrix — the workhorse of dimensionality reduction.
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Pseudoinverse
The Moore-Penrose generalization of a matrix inverse — exists for any matrix, even non-square or singular ones, and gives the least-squares solution.