6. Matrix Multiplication
The chapter discusses the efficient multiplication of matrices using dynamic programming techniques. It highlights the importance of the order of multiplication in determining the computational cost, with specific examples illustrating how different orders yield varying levels of efficiency. The chapter concludes with a discussion on formulating the problem inductively and filling up a cost matrix in a structured manner.
Enroll to start learning
You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- Matrix multiplication is associative but not commutative.
- The order in which matrices are multiplied can significantly affect the total computation cost.
- Dynamic programming can be applied to optimize the sequence of matrix multiplications.
Key Concepts
- -- Matrix Multiplication
- The operation of multiplying two matrices, requiring compatible dimensions where the number of columns of the first matrix equals the number of rows of the second.
- -- Dynamic Programming
- A method for solving complex problems by breaking them down into simpler subproblems, storing the results of these subproblems to avoid redundant computations.
- -- Computation Cost
- The total number of arithmetic operations required to achieve matrix multiplication, which can change based on the multiplication order.
- -- Cost Matrix
- A structured matrix that tracks the minimum number of operations required to multiply a specific sequence of matrices.
Additional Learning Materials
Supplementary resources to enhance your learning experience.