New posts in linear-transformations

Proof general state space similarity transformation to controllable canonical form

linear-transformations control-theory linear-control

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

linear-algebra abstract-algebra linear-transformations

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

linear-algebra proof-verification linear-transformations

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

linear-algebra matrices vector-spaces linear-transformations matrix-rank

Proving that L(V) cannot be finite dimensional given an identity.

linear-algebra linear-transformations

Annihilator of a vector space $V$ is the zero subspace of $V^*$

linear-algebra abstract-algebra linear-transformations dual-spaces

Why eigenvectors with the highest eigenvalues maximize the variance in PCA?

linear-algebra eigenvalues-eigenvectors linear-transformations machine-learning principal-component-analysis

Proving that $\operatorname{trace}(T) =\langle Te_1,e_1\rangle +\cdots+\langle Te_n,e_n\rangle $?

linear-algebra algebra-precalculus vector-spaces linear-transformations

Are non-degenerate bilinear forms equivalent to isomorphisms $V \cong V^*$?

linear-algebra linear-transformations multilinear-algebra bilinear-form

Green's Function / Impulse Response Confusion

ordinary-differential-equations linear-transformations greens-function

Theorem 9.34 Rudin

linear-algebra matrices analysis linear-transformations determinant

How to determine the Standard Matrix

linear-algebra linear-transformations

How to determine if some Linear Transformation exists

linear-algebra linear-transformations

Why Is $\sqrt{\det(A^TA)}$ A Volume / Volume Factor?

linear-algebra geometry determinant linear-transformations geometric-algebras

How do Integral Transforms work

definite-integrals linear-transformations laplace-transform fourier-transform inverse-laplace

Determine the Linear Transformation on the plane?

linear-algebra linear-transformations

If a symmetric matrix commutes with all symmetric matrices, is it then a multiple of the identity?

linear-algebra abstract-algebra matrices vector-spaces linear-transformations

How can I get eigenvalues of infinite dimensional linear operator?

functional-analysis operator-theory linear-transformations infinite-matrices

Given $T \in L(X,Y)$, show the equivalence between: existence of $S$ such that $S(T(x))=x$, and $T$ being injective with $T(X)$ complemented in $Y$

functional-analysis linear-transformations banach-spaces normed-spaces complete-spaces

Why are homogenous coordinates needed in image projection?

coordinate-systems linear-transformations