English
If α is a nonunital ring, the matrix algebra M_n(α) forms a nonunital ring.
Русский
Если α — неединичное кольцо, то алгебра матриц M_n(α) образует неединичное кольцо.
LaTeX
$$$\\mathrm{NonUnitalRing}\\big(\\mathrm{Matrix}_n(\\alpha)\\big)$$$
Lean4
/-- For two vectors `w` and `v`, `vecMulVec w v i j` is defined to be `w i * v j`.
Put another way, `vecMulVec w v` is exactly `replicateCol ι w * replicateRow ι v` for
`Unique ι`; see `vecMulVec_eq`. -/
def vecMulVec [Mul α] (w : m → α) (v : n → α) : Matrix m n α :=
of fun x y => w x * v y