Fast matrix pow function in lua (O(1) running time, for whatever n)

squaremat.lua

function m_pow(matrix, n)
	local a1 = -(matrix[1][1]+matrix[2][2])
	local a2 = (matrix[1][1]*matrix[2][2]-matrix[1][2]*matrix[2][1]) -- determinant
	-- r^2 + a1*r + a2 = 0, find rs -> (1/2)*(-a1 +- sqrt(a1^2 - 4*a2))
	local rt = math.sqrt(a1^2-4*a2)
	local r1 = (-a1+rt)/2
	local r2 = (-a1-rt)/2

	local r1n = r1^n
	local r2n = r2^n

	local b2 = (r2n-r1n)/(r2-r1)
	local b1 = (r2*r1n - r1*r2n)/(r2-r1)

	return {{b2*matrix[1][1]+b1, b2*matrix[1][2]}, {b2*matrix[2][1], b2*matrix[2][2]+b1}}

end

function print_matrix(matrix)
	print(unpack(matrix[1]))
	print(unpack(matrix[2]))
end

matrix = {{1,2},
		  {3,4}}
print_matrix(m_pow(matrix, 400))

take out the negative sign from a1 to make it even faster xdddddddddd

btw r2-r1 = -rt

oh and if rt is 0 then ull divide by zero lol

yeah, 0 gives me indeterminant for the identity matrix, or anytime when a+d = 2sqrt(ad-bc), rare cases though so I'm not gonna lose sleep :P

uh... if rt=0 then do it the normal way with a for loop or something?