query: What does a linear transformation do to a vector in $\mathbb{R}^2$ 1
positive_passages.docid: 150442
positive_passages.text: What does a linear transformation do to a vector in $\mathbb{R}^2$
negative_passages.docid: 63705
negative_passages.text: Show that rodriques formula is a linear transformation?
negative_passages.docid: 45416
negative_passages.text: linear transformation $T$ is onto if and only if $T^*$ is one to one
negative_passages.docid: 37813
negative_passages.text: If $T\colon \mathbb R^n \to \mathbb R^n $ linear and $T^2 = kT$
negative_passages.docid: 93121
negative_passages.text: How to prove there exists a linear transformation?
negative_passages.docid: 17087
negative_passages.text: Question concerning linear combinations of vectors and linear independence in Linear Algebra.
negative_passages.docid: 67498
negative_passages.text: Intuition behind the definition of linear transformation
negative_passages.docid: 47015
negative_passages.text: Vector Space Structures over ($\mathbb{R}$,+)
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 51209
negative_passages.text: A linear transformation satisfying $P^2 = P$
negative_passages.docid: 71492
negative_passages.text: Matrix of Linear Transformation by right multiplication
negative_passages.docid: 55420
negative_passages.text: How does the chain rule work for functions from vectors to vectors?
negative_passages.docid: 117986
negative_passages.text: Are there linear transformations from vector spaces over different fields?
negative_passages.docid: 54217
negative_passages.text: Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
negative_passages.docid: 112284
negative_passages.text: If $\mid a_{jj}\mid \gt \sum_{i \neq j} \mid a_{ij} \mid$ then vectors $a_1,\dots ,a_n \in \mathbb{R}^n$ are linearly indendent.
negative_passages.docid: 13903
negative_passages.text: mathematical difference between column vectors and row vectors
negative_passages.docid: 19964
negative_passages.text: What does the dot product of two vectors represent?