Theorems · Definition · linear algebra

LinearPMap.mkSpanSingleton

{K : Type u_7} →
  {L : Type u_8} →
    {E : Type u_9} →
      {F : Type u_10} →
        [inst : DivisionRing K] →
          [inst_1 : DivisionRing L] →
            {σ : K →+* L} →
              [inst_2 : AddCommGroup E] →
                [inst_3 : Module K E] →
                  [inst_4 : AddCommGroup F] → [inst_5 : Module L F] → (x : E) → F → x ≠ 0 → E →ₛₗ.[σ] F

The unique LinearPMap on span R {x} that sends a non-zero vector x to y. This version works for modules over division rings.

Defined in

Mathlib.LinearAlgebra.LinearPMap

Cited by

10 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingDivisionRingAddCommGroupModuleAddCommGroupModule