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Using echelon()" ], "created": "2024-10-05 20:21:29", "modified": "2024-10-05 20:21:29", "commits": 1 }, { "source": "a5-ginv.Rmd", "filename": "a5-ginv.html", "title": "Generalized inverse ", "author": "Michael Friendly", "engine": "knitr::rmarkdown", "headings": [ "Properties of generalized inverse (Moore-Penrose inverse)", "Rectangular matrices" ], "created": "2024-10-05 20:21:29", "modified": "2024-10-05 20:21:29", "commits": 1 }, { "source": "a6-inv-3d.Rmd", "filename": "a6-inv-3d.html", "title": "Linear transformations and matrix inverse in 3D ", "author": "Michael Friendly", "engine": "knitr::rmarkdown", "headings": [ "The unit cube", "Define some useful functions", "Show $\\mathbf{I}$ and $\\mathbf{A}$ all together in one figure", "Same, but using separate figures, shown side by side", "$A$ and $A^{-1}$", "Animate" ], "created": "2024-10-05 20:21:29", "modified": "2024-10-05 20:21:29", "commits": 1 }, { "source": "a7-eigen-ex1.Rmd", "filename": "a7-eigen-ex1.html", "title": "Eigenvalues and Eigenvectors: Properties ", "author": "Michael Friendly", "engine": "knitr::rmarkdown", "headings": [ "Setup", "Properties of eigenvalues and eigenvectors" ], "created": "2024-10-05 20:21:29", "modified": "2024-10-05 20:21:29", "commits": 1 }, { "source": "a8-eigen-ex2.Rmd", "filename": "a8-eigen-ex2.html", "title": "Eigenvalues: Spectral Decomposition ", "author": "Michael Friendly", "engine": "knitr::rmarkdown", "headings": [ "Setup", "Matrix factorization", "Spectral decomposition", "Further properties" ], "created": "2024-10-05 20:21:29", "modified": "2024-10-05 20:21:29", "commits": 1 }, { "source": "a9-linear-equations.Rmd", "filename": "a9-linear-equations.html", "title": "Solving Linear Equations ", "author": "Michael Friendly and John Fox", "engine": "knitr::rmarkdown", "headings": [ "Conditions for a solution", "Equations in two unknowns", "Two consistent equations", "Three consistent equations", "Three inconsistent equations", "Equations in three unknowns" 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