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

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

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

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

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

−1+(−24)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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