---
# System prepended metadata

title: Note on Linear Algebra
tags: [linear-algebra]

---

###### tags: `linear-algebra`


Note on Linear Algebra
===
- [Rank of a Matrix](/TOFVUiLnQvGd-w2KxWbZzw)
- [Particular and Homogeneous Holutions](/ZwEs0NAUSa6ZFFFFfF8Pfw)
- [Fundamental Theorems of Linear Algebra](/9XdaIiGaRuOHnhahrw-cpw)
- [Projection](/R8g_2yp5SrScLTZyK87qKw)
- [Invertible Matrix](/Ex5XG5h1RqyLb3Dy6CgZYQ)
- [Diagonalizable Matrix](/FZ0laYDATtKKQn3LM-AluQ)
- [Symmetric Matrix](/v-PmJxWLSu2wK0z-qTLxTQ)
- [Positive-definite Matrix](/ePYkaGOET_SLXES_a5LY0w)
- [Orthogonal Matrix](/ymOpRlTtQlGgTDXq2f2ltQ)
- [Similar Matrix](/1DKkKMUETvGU4hQ9PdSoVg)


Eigenvalues and eigenvectors
---
- [Eigenvalues and Eigenvectors](/GBF_aQypQ663uIQCAe2buw)

Decomposition
---
- [Jordan Form](/OFY0nD-0RRm-_p-Jcj80MA)
- [Rank Decomposition](/5sKfwHskQI2DmFsByE1y0Q)
- [LU Decomposition](/_nQeQBc_RiukZa3MSngJWg)
- [Jordan Decomposition](/txHw4Q92Srim6KYbBqWpIg)
- [Eigendecomposition](/XH8bHneRR6C4vfrWYDyOQA)
- [Cholesky Decomposition](/aAwngP20Sa-RhiUHGLSUMA)
- [QR Decomposition](/BP8u2tvsRqCwfBr0lMTmcQ)
- [Singular-value Decomposition](/sZjk4W-VQCiBPRv0axX8tg)
- [Schur Decomposition](/ggPBzGagTSO5bwtmdbMULQ)

Linear transformation
---


Applications
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- [Low-rank Approximation (Eckart–Young theorem)](/Z0t3H8mJQd6nLqv2Q-i8iA)
- [Ordinary Least Square](/RV-xGxoNR5a55aYWzvAotA)
- [Total Least Square](/4VkAIZXGRiiQTucWyDJ8tg)
- [Moore–Penrose Inverse](/LRDcM7GkTMu5lwl1DA52OA)
- [Quadratic Curves](/HxOSSauATFqdz2In2weidA)

Numerical linear algebra
---

- [Multiplication](/DVve_ArfQyqbEEXlVtF9Bw)
- [Transpose](/NVn9TQIZQEC1GdSB3zPq5g)

Miscellaneous
---
- [Gram–Schmidt Process](/ZRdTho_eSFuonEn1XrEQBA)
- [Name of Matrix](/u-gUuAQXQqCeOCZ35mi-gQ)

## Reference
[The-Art-of-Linear-Algebra](https://github.com/kenjihiranabe/The-Art-of-Linear-Algebra/tree/main)
[Immersive Linear Algebra](http://immersivemath.com/ila/tableofcontents.html)
[Interactive Linear Algebra](https://textbooks.math.gatech.edu/ila/systems-of-eqns.html)
[ULAFF](http://www.ulaff.net/)
[Nick Higham](https://nhigham.com/blog/)