Vector space, basis, span, orthogonality, orthonormality, and linear least square.Special matrices: square matrix, identity matrix, triangular matrix, the idea about sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian and unitary matrices.Eigenvalues, eigenvectors, diagonalization, and singular value decomposition.Matrix factorization concept/LU decomposition, Gaussian/Gauss-Jordan elimination, solving Ax=b linear system of an equation.Inner and outer products, matrix multiplication rule and various algorithms, and matrix inverse.Basic properties of a matrix and vectors: scalar multiplication, linear transformation, transpose, conjugate, rank, and determinant.Sometimes we do clustering of input by using spectral clustering techniques, and for this, we need to know eigenvalues and eigenvectors.īefore I discuss the Linear Algebra Courses, I would like to mention what topics in linear algebra you need to learn for data science and machine learning. For example in logistic regression, we do vector-matrix multiplication.
In machine learning, most of the time we deal with scalars and vectors, and matrices.
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