Find the Norm [[5,4,9],[-1,0,-1],[0,2,2],[-5,-4,-9]]

Problem

‖[5,4,9],[−1,0,−1],[0,2,2],[−5,−4,−9]‖_F

Solution

1. Identify the type of norm to be calculated. For a matrix A the Frobenius norm ∥A∥ is the square root of the sum of the squares of all its entries.

2. Square each individual element in the matrix.

5^2=25

4^2=16

9^2=81

(−1)^2=1

0^2=0

(−1)^2=1

0^2=0

2^2=4

2^2=4

(−5)^2=25

(−4)^2=16

(−9)^2=81

3. Sum all the squared values together.

25+16+81+1+0+1+0+4+4+25+16+81=254

4. Take the square root of the sum to find the final norm.

√(,254)

Final Answer

‖[5,4,9],[−1,0,−1],[0,2,2],[−5,−4,−9]‖_F=√(,254)

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