query: Rational scalar multiplication in Linear transformation using addition property
positive_passages.docid: 152379
positive_passages.text: If $V_1, V_2$ are $\mathbb{Q}$-vector spaces and $f \colon V_1 \to V_2$ is additive, then $f$ is $\mathbb{Q}$-linear
negative_passages.docid: 71492
negative_passages.text: Matrix of Linear Transformation by right multiplication
negative_passages.docid: 67498
negative_passages.text: Intuition behind the definition of linear transformation
negative_passages.docid: 111443
negative_passages.text: Optimization of $2x+3y+z$ under the constraint $x^2+ y^2+ z^2= 1$
negative_passages.docid: 125435
negative_passages.text: Practical application for linear transformations
negative_passages.docid: 65416
negative_passages.text: Is there a different way to define multiplication on Complex numbers?
negative_passages.docid: 102816
negative_passages.text: multiplication equivalent of the summation symbol
negative_passages.docid: 122202
negative_passages.text: How does the dot product convert a matrix into a scalar?
negative_passages.docid: 123220
negative_passages.text: Quick doubt about multiplying vectors by scalars
negative_passages.docid: 14161
negative_passages.text: Proof of when is $A=X^TX$ invertible?
negative_passages.docid: 121533
negative_passages.text: $3\times3$ linear system organization
negative_passages.docid: 2762
negative_passages.text: Mapping of zero vector under a linear transformation
negative_passages.docid: 69509
negative_passages.text: Showing a Linear Transformation is invertible
negative_passages.docid: 135571
negative_passages.text: Bézout Identity with coefficient divisibility constraints
negative_passages.docid: 88728
negative_passages.text: Dimensions of vector subspaces in a direct sum are additive
negative_passages.docid: 61998
negative_passages.text: Multiplying Taylor series and composition
negative_passages.docid: 108898
negative_passages.text: An Analogue of CRT for Polynomial Ring