query: Difference between number of scalars for proving linear transformations
positive_passages.docid: 23095
positive_passages.text: Prove that T is a linear transformation
negative_passages.docid: 71203
negative_passages.text: Proving that two systems of linear equations are equivalent if they have the same solutions
negative_passages.docid: 88013
negative_passages.text: injective linear transformation basis.
negative_passages.docid: 139868
negative_passages.text: Linear transformations, $R^5,R^4$
negative_passages.docid: 75855
negative_passages.text: Show that $\det{(A + sxy^*)}$ is linear in $s$
negative_passages.docid: 125435
negative_passages.text: Practical application for linear transformations
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
negative_passages.docid: 146984
negative_passages.text: Prove: Full Rank and a solution os linear system
negative_passages.docid: 115385
negative_passages.text: Computing matrices of linear transformation under different basis
negative_passages.docid: 27865
negative_passages.text: What is the number of invertible $n\times n$ matrices in $\operatorname{GL}_n(F)$?
negative_passages.docid: 80279
negative_passages.text: Show that $S + T$ and $aT$ are linear
negative_passages.docid: 66500
negative_passages.text: Proving that orthogonal vectors are linearly independent
negative_passages.docid: 33526
negative_passages.text: How to prove this beautiful statement on linear forms using induction?
negative_passages.docid: 104258
negative_passages.text: Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
negative_passages.docid: 59165
negative_passages.text: Derivative of a linear transformation.
negative_passages.docid: 117986
negative_passages.text: Are there linear transformations from vector spaces over different fields?
negative_passages.docid: 140225
negative_passages.text: Linear transformation maps the first quadrant to a closed set