Find the Norm

Problem

‖[1,−14,1,2,−2,−3],[2,−3,−1,−3,2,−1],[1,17,−4,1,1,−2],[−2,−52,−2,2,−1,−4],[3,24,−2,−1,1,3],[−1,−24,2,2,−1,−3]‖

Solution

1. Identify the type of norm to be calculated. Since no specific norm is mentioned for a matrix, the Frobenius norm (the square root of the sum of the squares of all elements) is the standard entry-wise norm.

2. Square every individual element in the matrix.

1^2+(−14)^2+1^2+2^2+(−2)^2+(−3)^2=1+196+1+4+4+9=215

2^2+(−3)^2+(−1)^2+(−3)^2+2^2+(−1)^2=4+9+1+9+4+1=28

1^2+17^2+(−4)^2+1^2+1^2+(−2)^2=1+289+16+1+1+4=312

−2^2+(−52)^2+(−2)^2+2^2+(−1)^2+(−4)^2=4+2704+4+4+1+16=2733

3^2+24^2+(−2)^2+(−1)^2+1^2+3^2=9+576+4+1+1+9=600

−1^2+(−24)^2+2^2+2^2+(−1)^2+(−3)^2=1+576+4+4+1+9=595

3. Sum the results from all rows.

215+28+312+2733+600+595=4483

4. Take the square root of the total sum to find the Frobenius norm.

√(,4483)

Final Answer

‖[1,−14,1,2,−2,−3],[2,−3,−1,−3,2,−1],[1,17,−4,1,1,−2],[−2,−52,−2,2,−1,−4],[3,24,−2,−1,1,3],[−1,−24,2,2,−1,−3]‖_F=√(,4483)

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