2 Rectangular Matrices

[[lecture-main-topic-data]]

We are particularly interested in the $d \times m$ matrix

G \sim N (0, 1)^{\otimes d \times m}

Concepts

File	status	type	Lectures
bound for the size of an epsilon packing	complete	🧮	Random Matrix Lecture 04
dimension requirements for gaussian random matrix to be a restricted isometry with high probability	complete	🧮	Random Matrix Lecture 05
distinguishing is equivalent to double nullspace property	complete	🧮	Random Matrix Lecture 05
epsilon faithful function	complete	💡	Random Matrix Lecture 03
epsilon net	complete	💡	Random Matrix Lecture 04
epsilon net restricted inner product bounds the operator norm	in progress	🧮	Random Matrix Lecture 04
epsilon packing	complete	💡	Random Matrix Lecture 04
first moment method	in progress	💡	Random Matrix Lecture 03
gaussian random matrix transforms vectors into gaussian random vectors	complete	🧮	Random Matrix Lecture 02 Random Matrix Lecture 03
Gram matrix	complete	💡	Lecture 22 Random Matrix Lecture 02
high probability bound for operator norm of difference for Gaussian covariance matrix	complete	🧮	Random Matrix Lecture 05 Random Matrix Lecture 04
high probability bound on singular values of gaussian random matrix	complete	🧮	Random Matrix Lecture 07 Random Matrix Lecture 04
Johnson-Lindenstrauss lemma	complete	🧮	Random Matrix Lecture 07 Random Matrix Lecture 03 Manifold Learning Lecture 05
joint of gaussian random transform of finite vectors	complete	🧮	Random Matrix Lecture 02
maximal epsilon packing is also a net	complete	🧮	Random Matrix Lecture 04
normalized gaussian random matrix preserves geometry in expectation	in progress	💡	Random Matrix Lecture 02
nullspace property	in progress		Random Matrix Lecture 05
random matrix	in progress	💡	Random Matrix Lecture 06 Random Matrix Lecture 09 Random Matrix Lecture 07 Random Matrix Lecture 02 Random Matrix Lecture 04
restricted inner product	in progress	💡	Random Matrix Lecture 04
restricted isometry implies nullspace property	complete	🧮	Random Matrix Lecture 05
restricted isometry property	complete	💡	Random Matrix Lecture 05
sparsity	complete	💡	Random Matrix Lecture 05
unique singular values yield unique outer product components	complete	🧮	Random Matrix Lecture 06
we can find an epsilon net with the bound for an epsilon packing	complete	🧮	Random Matrix Lecture 04

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