Linear algebra in ML
Vectors and Matrices
Vectors: Represented as a one-dimensional array of numbers. Used to represent data points, features, weights, etc.
Matrices: Represented as a two-dimensional array of numbers. Used to represent datasets, transformations, weights in neural networks, etc.
Operations
Addition and Subtraction: Element-wise operations for combining data.
Scalar Multiplication: Multiplying every element of a vector or matrix by a scalar.
Matrix Multiplication: Combining matrices to transform data, often used in neural networks and other models.
Linear Transformations
Matrix Multiplication: Represents linear transformations, which are fundamental in operations like scaling, rotating, and translating data.
Determinants and Inverses
Determinants: Used to understand properties of matrices, such as whether a matrix is invertible.
Inverses: Used in solving systems of linear equations, necessary for model training and optimization.
Eigenvalues and Eigenvectors
Eigenvalues: Scalars indicating the magnitude of transformation.
Eigenvectors: Vectors indicating the direction of transformation.
Principal Component Analysis (PCA): Uses eigenvectors and eigenvalues for dimensionality reduction.
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