List questions from linear-transformations

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Which ones of these two shows that the tensor product operation on two multilinear functions is bilinear?

Published on 14 Nov 2018 - 23:20

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Does transformation invariance of the range and null space imply commutativity?

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Inner Product with a Linear Transformation

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Explain the geometrical meaning of Singular Value Decomposition (SVD)

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What is the geometrical significance of a complex-valued singular value decomposition?

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$(I-A)^{-1}=\sum_{i=0}^\infty A^i$

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Characteristic polynomial of a linear operator in matrix space

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Linear transformation of a hyperplane

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Orthogonal Projection onto Range of Matrix

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Prove that the nullspaces of linear operators acting on themselves are eventually equal

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Let ${^ts}:E\to F$ be the transpose of $s:F\to E$. Show that $\text{Im}(s)\cap \ker (\,^ts)=\{0_E\}$.

Published on 25 Mar 2026 - 4:42

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Shift Operator and Invariant Subspace

Published on 16 Nov 2018 - 18:20

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Show that the linear map $T:P_3(\Bbb R)→\Bbb R^4, p↦(p(0),p(1),p′(0),p′(1))$ is an isomorphism.

Published on 16 Nov 2018 - 22:50

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Find $T^*(x,y)$ with the given inner product

Published on 26 Mar 2026 - 7:33

List Question

Geometric Meaning of the Jacobian of a Linear Transformation

Which ones of these two shows that the tensor product operation on two multilinear functions is bilinear?

Does transformation invariance of the range and null space imply commutativity?

Inner Product with a Linear Transformation

Explain the geometrical meaning of Singular Value Decomposition (SVD)

What is the geometrical significance of a complex-valued singular value decomposition?

$(I-A)^{-1}=\sum_{i=0}^\infty A^i$

Characteristic polynomial of a linear operator in matrix space

Linear transformation of a hyperplane

Orthogonal Projection onto Range of Matrix

Prove that the nullspaces of linear operators acting on themselves are eventually equal

Let ${^ts}:E\to F$ be the transpose of $s:F\to E$. Show that $\text{Im}(s)\cap \ker (\,^ts)=\{0_E\}$.

Shift Operator and Invariant Subspace

Show that the linear map $T:P_3(\Bbb R)→\Bbb R^4, p↦(p(0),p(1),p′(0),p′(1))$ is an isomorphism.

Find $T^*(x,y)$ with the given inner product

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