[Verse 1]
Matrices multiplyin', complexity buildin' high
Standard algorithm got that cubic time to cry
But Strassen stepped up with a mathematical scheme
Seven multiplications, recursive dream
Split your matrices into blocks of equal size
Two by two partitions, watch the magic in your eyes
Where others see sixteen mults, he spotted just seven
Asymptotic glory, computational heaven
[Chorus]
Seven mults instead of eight, that's the Strassen way
Divide and conquer, recursive play
A-eleven, A-twelve, A-twenty-one, A-twenty-two
Block by block we're breakin' through
Seven products, P-one through seven
Matrix multiplication redefined in heaven
[Verse 2]
P-one equals A-eleven times B-twelve minus B-twenty-two
P-two takes A-eleven plus A-twelve times B-twenty-two
P-three multiplies A-twenty-one plus A-twenty-two with B-eleven
P-four needs A-twenty-two times B-twenty-one minus B-eleven
Each product calculated with recursion in the flow
Submatrices dividin' till they're small enough to go
[Chorus]
Seven mults instead of eight, that's the Strassen way
Divide and conquer, recursive play
A-eleven, A-twelve, A-twenty-one, A-twenty-two
Block by block we're breakin' through
Seven products, P-one through seven
Matrix multiplication redefined in heaven
[Bridge]
P-five through P-seven complete the calculation
Complex combinations, mathematical sensation
C-eleven gets P-one plus P-four minus P-five plus P-seven
C-twelve receives P-three plus P-five, algorithmic heaven
Time complexity drops from n-cubed to log-of-seven
Two-point-eight-oh-seven, efficiency's new weapon
[Verse 3]
Base case handles small matrices with standard computation
Threshold optimization prevents stack constitution
Memory overhead trades with computational gains
Numerical stability sometimes breaks the chains
But when matrices grow massive, Strassen claims the crown
Logarithmic improvement brings the runtime down
[Outro]
Seven sacred products, recursive revelation
Strassen's contribution to computational innovation
From cubic down to log-base-two-of-seven power
Matrix multiplication's finest algorithmic hour