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In polar decomposition, the Q corresponds to UVT in SVD, why?

Lecture 6

proof

Status: Open.

#9 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 20, 2023

When i is greater than r(r=rank) in SVD, what are the components of u_i and v_i?

Lecture 6

proof

Status: Open.

#8 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 20, 2023

Why does it matter if the eigen value is double, triple in A*v=sigma * u?

Lecture 6

proof

Status: Open.

#7 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 20, 2023

Why does the professor explain with A*v = sigma*u?

Lecture 6

proof

Status: Open.

#6 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 20, 2023

Why is AA^T positive definite?

Lecture 6

proof

Status: Open.

#5 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 20, 2023

Why is orthogonal matrix important?

etc

Lecture 3

Status: Open.

#4 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 13, 2023

summary for Symmetric eigendecomposition & Non Symmetric eigendecomposition

Lecture 2

theorem

Status: Open.

#3 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 11, 2023

proof for N(A) = n-r, N(A^T) = m-r.

Lecture 2

proof

Status: Open.

#2 In Mathematics-for-ML/MIT-18.065-Linear-Algebra;

· changhyeonnam opened on Jan 11, 2023