List questions from numerical-linear-algebra

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Suppose ||.|| is an induced matrix norm, A is non-singular, and B is singular. Prove $\frac{1}{\kappa(A)}\leq\frac{||A-B||}{||A||}$.

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Matrix equation of the form $C A C^\intercal = D$

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What does $\max_{i,j} \langle\phi_{i}, \psi_{j}\rangle$ mean in mathematics?

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Numerically determine eigenvalues of real non-symmetric matrix known to have positive eigenvalues

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Uniqueness of a solution of a matrix

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Forward stability

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Preconditioning the Damped Normal Equations - Reference

Published on 10 May 2026 - 13:45

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Condition number bound using block LU factorization

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Why is this having numerical stability issues?

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Minimization version of matrix p-norms?

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Projecting a vector onto its span

Published on 14 May 2026 - 20:54

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When does it make sense to model data as lying on a union of subspaces?

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How to quickly determine whether the intersection of two linear subspaces contain nonzero vectors?

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Solving an inequality containing Legendre polynomials

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List Question

Derivatives of Approximate Matrix inverses

Suppose ||.|| is an induced matrix norm, A is non-singular, and B is singular. Prove $\frac{1}{\kappa(A)}\leq\frac{||A-B||}{||A||}$.

Matrix equation of the form $C A C^\intercal = D$

What does $\max_{i,j} \langle\phi_{i}, \psi_{j}\rangle$ mean in mathematics?

Numerically determine eigenvalues of real non-symmetric matrix known to have positive eigenvalues

Uniqueness of a solution of a matrix

Forward stability

Preconditioning the Damped Normal Equations - Reference

Condition number bound using block LU factorization

Why is this having numerical stability issues?

Minimization version of matrix p-norms?

Projecting a vector onto its span

When does it make sense to model data as lying on a union of subspaces?

How to quickly determine whether the intersection of two linear subspaces contain nonzero vectors?

Solving an inequality containing Legendre polynomials

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