Articles

A detailed exploration of Kernel Principal Component Analysis (Kernel PCA), explaining its necessity, the underlying 'kernel trick', and how it extends PCA to handle non-linear data structures.

A detailed guide on representation learning, focusing on why a line is a good representation, how to find the best proxy for a point, and a full derivation to find the optimal line that minimizes reconstruction error (PCA).

A detailed explanation of the Gram-Schmidt process, including its purpose, step-by-step procedure, and multiple examples from vector spaces to function spaces.

A comprehensive guide to NumPy array manipulation, from basic indexing and slicing to advanced techniques with fancy indexing, boolean masking, and the powerful np.where() function. Includes 20 challenging practice problems.

A detailed, step-by-step guide to understanding Singular Value Decomposition (SVD) from first principles, complete with geometric intuition and solved problems.

An intuitive, step-by-step explanation of eigen decomposition, showing how it simplifies complex matrix transformations by changing to a special basis where the action is just simple scaling.

An in-depth look at symmetric matrices, exploring their key properties like real eigenvalues and orthogonal eigenvectors, the Spectral Theorem, and the geometric interpretation of their transformations.

A detailed article explaining how eigenvalues and eigenvectors reveal the geometric nature of a linear transformation, including scaling, rotation, reflection, and shearing.

A comprehensive, step-by-step tutorial on how to calculate eigenvectors and eigenvalues, complete with 10 detailed solved problems for 2x2 and 3x3 matrices.

An in-depth guide to understanding the algebraic and geometric multiplicity of eigenvalues, their relationship, and why this distinction is crucial for concepts like matrix diagonalization.