Uploaded August 2026 | Updated September 2026, 2 weeks ago
NumPy turns the machinery of linear algebra into fast, readable Python.
In this lesson, we use NumPy’s linear algebra module to calculate determinants and inverses, identify singular matrices, find eigenvalues and eigenvectors, and solve systems of linear equations. We also examine why numpy.linalg.solve() is preferable to explicitly calculating a matrix inverse.
Then we move into matrix decompositions—including singular value decomposition—and finish with a practical application: using principal component analysis to reduce five-dimensional data to three dimensions while preserving most of its information.
Along the way, we cover:
• Determinants, inverses, and identity matrices
• Singular matrices and systems without unique solutions
• Eigenvalues and eigenvectors
• Complex eigenvalues from rotation matrices
• Solving small and large systems of equations
• Numerical stability and floating-point error
• Singular value decomposition (SVD)
• Eigen decomposition
• Principal component analysis (PCA)
• Dimensionality reduction and reconstruction error
Your CPU has suffered through enough inefficient matrix arithmetic.
Chapters
00:00 Linear Algebra Optimization Protocol
00:34 NumPy arrays and linear algebra
01:25 Determinants and inverses
02:37 Eigenvalues and eigenvectors
04:10 Solving systems of equations
06:22 Matrix decompositions
08:16 Principal component analysis
10:51 Summary
Support Socratica on Patreon:
patreon.com/socratica
NumPy turns the machinery of linear algebra into fast, readable Python.
In this lesson, we use NumPy’s linear algebra module to calculate determinants and inverses, identify singular matrices, find eigenvalues and eigenvectors, and solve systems of linear equations. We also examine why numpy.linalg.solve() is preferable to explicitly calculating a matrix inverse.
Then we move into matrix decompositions—including singular value decomposition—and finish with a practical application: using principal component analysis to reduce five-dimensional data to three dimensions while preserving most of its information.
Along the way, we cover:
• Determinants, inverses, and identity matrices
• Singular matrices and systems without unique solutions
• Eigenvalues and eigenvectors
• Complex eigenvalues from rotation matrices
• Solving small and large systems of equations
• Numerical stability and floating-point error
• Singular value decomposition (SVD)
• Eigen decomposition
• Principal component analysis (PCA)
• Dimensionality reduction and reconstruction error
Your CPU has suffered through enough inefficient matrix arithmetic.
Chapters
00:00 Linear Algebra Optimization Protocol
00:34 NumPy arrays and linear algebra
01:25 Determinants and inverses
02:37 Eigenvalues and eigenvectors
04:10 Solving systems of equations
06:22 Matrix decompositions
08:16 Principal component analysis
10:51 Summary
Support Socratica on Patreon:
patreon.com/socratica
