The correlation coefficient (r) ranges from -1 to +1, indicating the strength and direction of the relationship between two variables. It can be calculated using the formula: r = (n * (Σxy) - (Σx)(Σy)) / sqrt([(n * Σx² - (Σx)²) * (n * Σy² - (Σy)²)]).

Covariance measures the direction of linear relationship between variables, while correlation standardizes this measure to indicate both direction & strength. Covariance can be positive, negative or zero, whereas correlation ranges from -1 to 1.

In machine learning, understanding the bias-variance tradeoff is crucial for building robust models. It balances model complexity & prediction accuracy, ensuring algorithms perform well on both training & unseen data.

Linear regression predicts continuous dependent variable based on one or more independent variables. Types include simple, multiple & polynomial linear regression. Python implementation using numpy & matplotlib is provided for each type.

Mean: average value, Variance: measures dispersion from mean, Standard Deviation: square root of variance, crucial in engineering & data analysis for quality control, signal processing & reliability engineering.

SVD decomposes matrices into U, Σ, and V^T components, simplifying complex data for analysis and insights.

Eigen decomposition breaks down a square matrix into eigenvalues & eigenvectors, simplifying complex calculations. It's crucial for physics, machine learning & computer graphics, and used in tasks like PCA, image compression & enhancement.

LU decomposition breaks down a square matrix into lower (L) and upper (U) triangular matrices, simplifying solving systems of linear equations and computing matrix inverses.

Gaussian Elimination solves systems of linear equations by transforming the matrix into upper triangular form (row echelon form) using forward elimination & back substitution. Implemented in Python with O(N³) time complexity.

Matrices are a fundamental concept in math & computer science used for solving equations, simulations & transformations. Learn the essentials of matrices, their operations & how to work with them programmatically.

Systems of linear equations are fundamental in programming, used for modeling relationships between variables and solving real-world problems like optimizing resources or simulating physical systems.