New posts in matrix-decomposition

How to understand the spectral decomposition geometrically?

linear-algebra matrices spectral-theory matrix-decomposition

Understanding the singular value decomposition (SVD)

linear-algebra matrices matrix-decomposition svd

Relation between Cholesky and SVD

matrices eigenvalues-eigenvectors matrix-decomposition svd cholesky-decomposition

Why is the non-negative matrix factorization problem non-convex?

matrices optimization convex-analysis matrix-decomposition non-convex-optimization

Why do we say SVD can handle singular matrix in least-squares? Comparison of SVD and QR decompositions

matrices numerical-linear-algebra matrix-decomposition least-squares svd

How is the null space related to singular value decomposition?

linear-algebra matrix-decomposition svd

A normal matrix with real eigenvalues is Hermitian

linear-algebra matrices eigenvalues-eigenvectors matrix-decomposition hermitian-matrices

LU Decomposition vs. Cholesky Decomposition

linear-algebra matrices matrix-decomposition lu-decomposition cholesky-decomposition

Let $A=(a_{ij})$ be an $n\times n$ matrix. Suppose that $A^2$ is diagonal. Must $A$ be diagonal?

linear-algebra matrices matrix-decomposition

When does a Square Matrix have an LU Decomposition?

matrices algorithms matrix-decomposition

Problem with Singular Value Decomposition

linear-algebra matrix-decomposition

Polar decomposition of real matrices

linear-algebra matrix-decomposition

Computing the Smith Normal Form

matrices finite-groups abelian-groups matrix-decomposition smith-normal-form

Proof that $\text{det}(AB) = \text{det}(A)\text{det}(B)$ without explicit expression for $\text{det}$

linear-algebra matrices eigenvalues-eigenvectors determinant matrix-decomposition

How can you explain the Singular Value Decomposition to non-specialists?

linear-algebra matrices matrix-decomposition svd singular-values

Calculating SVD by hand: resolving sign ambiguities in the range vectors.

linear-algebra matrices eigenvalues-eigenvectors matrix-decomposition svd

If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$

linear-algebra matrices trace matrix-decomposition

How unique are $U$ and $V$ in the Singular Value Decomposition?

linear-algebra matrices matrix-decomposition svd singular-values