query: If the images of vectors are linearly dependent, then they are linearly dependent
positive_passages.docid: 143149
positive_passages.text: Can linearly independent vectors have linearly dependent images?
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 131132
negative_passages.text: Proofs using vector properties
negative_passages.docid: 96394
negative_passages.text: Measure of Image of Linear Map
negative_passages.docid: 96354
negative_passages.text: Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
negative_passages.docid: 139951
negative_passages.text: Direct Sum of vector subspaces
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$
negative_passages.docid: 153028
negative_passages.text: Showing that the product of vector magnitudes is larger than their dot product
negative_passages.docid: 19846
negative_passages.text: Gram matrix invertible iff set of vectors linearly independent
negative_passages.docid: 91087
negative_passages.text: For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
negative_passages.docid: 6291
negative_passages.text: Proving something is a linearly independent subset
negative_passages.docid: 97281
negative_passages.text: Question regarding matrices with same image
negative_passages.docid: 93910
negative_passages.text: Equality in Cauchy-Schwarz Inequality implies linear dependence.
negative_passages.docid: 152147
negative_passages.text: Why is a set of orthonormal vectors linearly independent?
negative_passages.docid: 61281
negative_passages.text: Finding maximal sublist of linearly independent vectors
negative_passages.docid: 113326
negative_passages.text: Proving orthogonality of vectors in a complex vector space
negative_passages.docid: 143187
negative_passages.text: Matrix power series has linearly dependent terms