What is cost of matrix multiplication?

What is cost of matrix multiplication?

The cost of a single triangle in terms of the number of multiplications needed is the product of its vertices. The total cost of a particular triangulation of the polygon is the sum of the costs of all its triangles: (AB)C: (10×30×5) + (10×5×60) = 1500 + 3000 = 4500 multiplications.

What is the minimum number of scalar multiplications required to multiply a chain of matrices with a dimension vector p =< 5 2 3 4 7 >?

Explanation: The minimum number of multiplications required is 7750.

How do you solve matrix chain multiplication problems?

Example of Matrix Chain Multiplication

1. Example: We are given the sequence {4, 10, 3, 12, 20, and 7}.
2. Now product of 3 matrices:
3. M [1, 3] =264.
4. M [2, 4] = 1320.
5. M [1, 4] =1080.
6. Now Product of 5 matrices:
7. Final Output is:
8. Step 3: Computing Optimal Costs: let us assume that matrix Ai has dimension pi-1x pi for i=1, 2, 3….n.

How many ways can n matrices be multiplied?

there are total 5 ways to multiply 4 matrices.

Can matrices be simplified?

Matrices of the same order can be added or subtracted. For matrix simplification, put all the values of individual matrices into equations within one big matrix and then perform the required operation, i.e. addition or subtraction. Therefore, solving the matrices gives a single simplified matrix.

When can you multiply matrices?

You can only multiply two matrices if their dimensions are compatible , which means the number of columns in the first matrix is the same as the number of rows in the second matrix.

How do you find the cost matrix?

Sidenote: a perhaps more straightforward definition of a cost matrix would be ¯Gm m = G(m -m) m, the sum of squared residuals for a segment from m to m/ − 1.

What is a cost matrix?

Definition. A Cost Matrix is a method for adjusting the weight assigned to misclassifications by Credit Scoring Models in particular supervised models. The cost matrix offers a means to differentiate the importance of Type I and Type II classification errors.

What is the minimum number of scalar multiplications required to multiply a chain of matrices?

1500
Question 1 Explanation: → The minimum number of scalar multiplications required is 1500.

What is the minimum number of multiplications involved in computing the matrix product PQR?

16
∴ The minimum number of multiplications involved in computing the matrix product PQR = 16.

How to multiply matrices with a minimum number of multiplications?

The minimum number of multiplications are obtained by putting parenthesis in following way ( (AB)C)D –> 10*20*30 + 10*30*40 + 10*40*30 Input: p [] = {10, 20, 30} Output: 6000 There are only two matrices of dimensions 10×20 and 20×30. So there is only one way to multiply the matrices, cost of which is 10*20*30

Which parenthesization of a matrix requires less number of operations?

Clearly the first parenthesization requires less number of operations. Given an array p [] which represents the chain of matrices such that the ith matrix Ai is of dimension p [i-1] x p [i]. We need to write a function MatrixChainOrder () that should return the minimum number of multiplications needed to multiply the chain.

Is the multiplication of two matrices commutative?

The matrix multiplication is not commutative. In matrix multiplication, the order matters a lot. This shows that the matrix AB ≠BA. Hence, the multiplication of two matrices is not commutative. If A, B and C are the three matrices, the associative property of matrix multiplication states that,

What if the product of two matrices is a zero matrix?

If the product of two matrices is a zero matrix, it is not necessary that one of the matrices is a zero matrix. Let’s consider a simple 2 × 2 matrix multiplication A = [3 7 4 9] [ 3 7 4 9] and another matrix B = [6 2 5 8] [ 6 2 5 8]