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Let $V$ be a finite dimensional vector space and $S,T:V \rightarrow V$ be linear. Is $ dim(S(ImT)) = rank (ST)$?

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#linear-algebra #vector-spaces #linear-transformations
255
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Find linear transformation whose kernel is given

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#linear-algebra #linear-transformations #smooth-functions
2.6k
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Calculating matrix for linear transformation of orthogonal projection onto plane.

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#linear-algebra #linear-transformations
38
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Show that K>0 is an eigenvalue by finding an Eigenvecter corresponding to k

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#linear-algebra #eigenvalues-eigenvectors #linear-transformations
1k
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Linear transformation: Reflecting a point about a line in $\mathbb R^3$.

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#linear-algebra #matrices #geometry #linear-transformations
102
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If the images of vectors are linearly dependent, then they are linearly dependent

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#linear-algebra #linear-transformations
23
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row reduced form with element $i$

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#linear-algebra #matrices #linear-transformations
108
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Prove this matrix inequality

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#linear-algebra #linear-transformations #positive-definite #symmetric-matrices
2.3k
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Existence of a vector $v$ in $V$ such that the $T$-annihilator of $v$ is the minimal polynomial for $T$.

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#linear-algebra #solution-verification #linear-transformations #minimal-polynomials
2.4k
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Can a $2 \times 3$ matrix be full rank?

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#linear-algebra #matrices #linear-transformations #matrix-rank
1k
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Showing that image of a certain linear map is either trivial or a straight line

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#linear-algebra #functions #linear-transformations
39
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Which are linear transformations?

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#linear-algebra #vector-spaces #linear-transformations
91
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Proofs with linear maps

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#linear-algebra #proof-writing #linear-transformations
113
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Properties of bounded linear operators between two normed spaces

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#functional-analysis #linear-transformations #normed-spaces
45
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Does $D$ have real eigenvalues?

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#linear-algebra #eigenvalues-eigenvectors #linear-transformations

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