Linear algebra notebook
We use a notebook for doing computation, finding examples, or taking notes. The idea of this Linear Algebra Notebook (LA-notebook) follows the same philosophy: Whenever you encounter a new mathematical object, you should play with it by doing some computation , run some examples to see its behaviors (both examples or counterexamples!), and then write down the notes just for yourself . This process is like conducting experiments in your mind, where your brain is analyzing the mathematical objects.
Take a awesome note for yourself, so that you can easily review what your brain has done in the future!
To download the LA-notebook:Visit LA-notebook Releases and download the latest version; newer versions are at the top, and you may click on “Source code (zip)” to download it.
You need Jupyter with the SageMath kernel to open the files.
You may choose one of the following two methods.
ipynb
files in the LA-notebook.If you are not able to install SageMath on your machine, or you wish to use the browser version of it. You may run the files through CoCalc as follows.
LA-notebook.zip
you downloaded in Step 2.zip
to extract it.(The links below are read-only. Follow the instructions above if you wish to run the code inside a file.)
a. Sage: Matrices and linear equations
Basic geometry & subspaces
101 --> 102 --> {103, 104} --> 105
Affine subspace & solutions
(102 -->)
106 --> 107 --> 108 --> {109, 110} --> 111
Topics
112, 113, 114, 10a
Spaces in Rn
201 --> 202 --> {203, 204} --> 205 --> 206 --> 207
Abstract spaces
208 --> 209 --> 210
Operations of spaces
211 --> 212
Inner product space
213 --> 214 --> 215
Linear function
301 --> 302 --> 303 -->304
Vector and matrix representations
305 --> 306 --> 307 --> 308 --> 309 --> 310
Topics
311, 312, 313, 314, 315
Determinant for small matrices
401
Geometric interpretations
402 --> {403, 404}
Definition and properties
405 --> {406, 407, 408} --> 409
Adjugate
410 --> 411
Permutation expansion
412 --> 413 --> {414, 415}
a. Python: NumPy and numerical linear algebra
Good basis
501 --> {502, 503, 504, 505}
Characteristic polynomial
506 --> 507
Diagonalization
508 --> 509 --> 510
Topics
511, 512, 513, 514, 50a
Schur triangulation
601 --> 602 --> 603 --> 604 --> 605 --> 606
Symmetric matrix
607 --> 608 --> 609 --> 610 --> 611
Statistics
612 --> 613
Laplacian matrix
614 --> 615
A. Index with translations