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28 Bookmarks

Why study Algebraic Geometry?

Teaching myself differential topology and differential geometry

How to intuitively understand eigenvalue and eigenvector?

Why study linear algebra?

Importance of matrix rank

A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum

String Theory: What to do?

Geometric interpretation for complex eigenvectors of a 2×2 rotation matrix

How to take the gradient of the quadratic form?

Can a real symmetric matrix have complex eigenvectors?

Why are all nonzero eigenvalues of the skew-symmetric real matrices pure imaginary?

Eigenvalues are unique?

How to understand the spectral decomposition geometrically?

A unitary matrix taking a real matrix to another real matrix, is it an orthogonal matrix?

What does linear dependence (among vectors) actually mean geometrically?

Linear Algebra Question ( rank of matrix )

Question 5 from Summer 2012 Exam Course 20109

Minimization under condition

Are Jordan chains always linearly independent?

A matrix with the property $\mathrm{tr}(A^{m})=0$ for every $m$ is nilpotent? [duplicate]

How is the dotproduct a projection?

Question on Linear Algebra

How to show $(A^{T}A)^{2}=A^{T}A$, where A is a matrix.

Dimension of least squares solution

Let $M_{2\times 2}$ be the vector space of all $2\times 2$ matrices. Show that the set of non-singular matrices is NOT a subspace.

Why is every solution to a homogenous second-order linear differential equation in the form $C_0e^{\alpha x} + C_1e^{\beta x}$

Bases and Dimension

Jordan Canonical form of a matrix over rationals whose all entries are 1.