English
Scalar multiplying a block matrix distributes across all four blocks: x • fromBlocks A B C D = fromBlocks (x • A) (x • B) (x • C) (x • D).
Русский
Умножение на скаляр блокированной матрицы distributes по всем четырём блокам: x • fromBlocks A B C D = fromBlocks (x • A) (x • B) (x • C) (x • D).
LaTeX
$$$ x \\cdot \\text{fromBlocks } A B C D = \\text{fromBlocks }(x \\cdot A) (x \\cdot B) (x \\cdot C) (x \\cdot D) $$$
Lean4
theorem fromBlocks_smul [SMul R α] (x : R) (A : Matrix n l α) (B : Matrix n m α) (C : Matrix o l α) (D : Matrix o m α) :
x • fromBlocks A B C D = fromBlocks (x • A) (x • B) (x • C) (x • D) := by ext i j;
rcases i with ⟨⟩ <;> rcases j with ⟨⟩ <;> simp [fromBlocks]
