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Do I need to know linear algebra for data science?
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This is an essential branch of mathematics for understanding how machinelearning algorithms work on a stream of data to create insight. Everything from friend suggestions on Facebook, to song recommendations on Spotify, to transferring your selfie to a Salvador Dali-style portrait using deep transfer learning involves matrices and matrix algebra. Here are the essential topics to learn:

- Basic properties of matrix and vectors: scalar multiplication, linear transformation, transpose, conjugate, rank, determinant
- Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse
- Special matrices: square matrix, identity matrix, triangular matrix, idea about sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian and unitary matrices
- Matrix factorization concept/LU decomposition, Gaussian/GaussJordan elimination, solving $\mathrm{Ax}=\mathrm{b}$ linear system of equation
- Vector space, basis, span, orthogonality, orthonormality, linear least square
- Eigenvalues, eigenvectors, diagonalization, singular value decomposition

Where You Might Use It
If you have used the dimensionality reduction technique principal component analysis, then you have likely used the singular value decomposition to achieve a compact dimension representation of your data set with fewer parameters. All neural network algorithms use linear algebra techniques to represent and process network structures and learning operations.

by Platinum (132,156 points)

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