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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
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