What is the rank of a linear transformation $f: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ such that $ \operatorname{Ker} f \leqslant \operatorname{Im}f$?

score 108 · Answer 10 · 2026-03-22 10:22:16

108

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score 191 · Answer 11 · 2026-03-22 17:41:15

191

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score 85 · Answer 12 · 2026-03-26 14:29:27

85

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Geometric Intuition for the Existence of Eigenvectors

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score 944 · Answer 13 · 2026-03-23 04:03:16

944

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Injective linear map is surjective then vector space is finite

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score 75 · Answer 14 · 2026-03-19 15:50:57

75

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Composition of regularized inverse of linear operator on dense subspace converges on whole space?

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score 42 · Answer 15 · 2026-03-25 18:32:12

42

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How is the homogeneous solution of a linear different equation "transformed" using method of undetermined coefficients?

Published on 25 Mar 2026 - 18:32

List Question

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What is the rank of a linear transformation $f: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ such that $ \operatorname{Ker} f \leqslant \operatorname{Im}f$?

Show that T - I is a projection.

Find the mapping of the curve by linear transformation

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Composition of regularized inverse of linear operator on dense subspace converges on whole space?

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