Newbetuts

Dimension of $\mathbb{Q}$-vector space if a nonsingular linear transformation $T$ exists such that $T^{-1} = T^{2} + T$

Prove that $\text{rank } T = \operatorname{rank} T^2 \iff \operatorname{Im}T \cap \ker T = \{ \vec 0\}$

Find linear transformation given kernel

Are the eigenvectors of a real symmetric matrix always an orthonormal basis without change?

Dimension of commutator space of matrices (again)

Generalizing Determinants Through Multilinear Algebra and Immanants

Sum of singular values of a matrix

Coordinate free proof that det is algebraic

Dimension of a Subspace of $\text{Hom}_\mathbb{K}(\mathcal{V},\mathcal{W})$ Consisting of Only Linear Transformations of Rank $\leq r$

Eigenvalue bound for quadratic maximization with linear constraint

How to construct abstractly and symmetrically the map $𝛬^{n+k}M⊗𝛬^kN→𝛬^nM$ given a pairing $M⊗N→R$?

If the dot product between two vectors is $0$, are the two linearly independent?

Surjectivity of a map between a module and its double dual

Prove that all nxn nilpotent matrices of order n are similar.

Finding rotation of 3 given lines in 3D until intersection with 3 other given lines

New posts in linear-algebra

Dimension of $\mathbb{Q}$-vector space if a nonsingular linear transformation $T$ exists such that $T^{-1} = T^{2} + T$

Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?

Basis for Skew Symmetric Matrix

Eigenvalues of $MA$ versus eigenvalues of $A$ for orthogonal projection $M$

Prove that the group $\mathrm{GL}(n, \mathbb{Z})$ is finitely generated [duplicate]

Necessary and sufficient conditions for left and right eigenvectors to be equal

Prove that $\text{rank } T = \operatorname{rank} T^2 \iff \operatorname{Im}T \cap \ker T = \{ \vec 0\}$

Find linear transformation given kernel

Are the eigenvectors of a real symmetric matrix always an orthonormal basis without change?

Dimension of commutator space of matrices (again)

Generalizing Determinants Through Multilinear Algebra and Immanants

Sum of singular values of a matrix

Coordinate free proof that det is algebraic

Dimension of a Subspace of $\text{Hom}_\mathbb{K}(\mathcal{V},\mathcal{W})$ Consisting of Only Linear Transformations of Rank $\leq r$

Eigenvalue bound for quadratic maximization with linear constraint

How to construct abstractly and symmetrically the map $𝛬^{n+k}M⊗𝛬^kN→𝛬^nM$ given a pairing $M⊗N→R$?

If the dot product between two vectors is $0$, are the two linearly independent?

Surjectivity of a map between a module and its double dual

Prove that all nxn nilpotent matrices of order n are similar.

Finding rotation of 3 given lines in 3D until intersection with 3 other given lines