Linear Algebra Glossary
Foundational to advanced terms in linear algebra for machine learning
- Scalar - A single number with no direction, used to scale vectors and matrices.
- Vector - An ordered list of numbers, representing a point or direction with magnitude.
- Matrix - A rectangular grid of numbers arranged in rows and columns.
- Tensor - A generalization of scalars, vectors, and matrices to any number of dimensions.
- Vector Addition - Combining two equal-length vectors by adding entries elementwise.
- Scalar Multiplication - Multiplying every entry of a vector or matrix by the same scalar.
- Dot Product - A scalar produced by elementwise-multiplying two equal-length vectors and summing.
- Magnitude - The length of a vector: square root of the sum of squared entries.
- Unit Vector - A vector with magnitude exactly 1, obtained by dividing by its own magnitude.
- Transpose - The matrix obtained by swapping rows and columns.
- Identity Matrix - The square matrix with 1s on the diagonal and 0s elsewhere; the matrix no-op.
- Matrix Multiplication - Combining an m×k matrix and a k×n matrix into an m×n matrix of row-column dot products.
- Linear Combination - A sum of vectors each multiplied by a scalar coefficient.
- Vector Norm - A function assigning a non-negative size to a vector, generalizing length.
- Orthogonality - Two vectors are orthogonal when their dot product is zero (90° angle).