Find the Norm

Problem

‖[1,−1,−1,−5],[−3,2,4,−1],[−10,10,11,12],[13,14,15,16]‖

Solution

1. Identify the type of norm to be calculated. In the absence of a specific subscript, the Frobenius norm (∥A∥ is the standard entry-wise norm for a matrix.

2. Square every individual entry in the matrix.

1+(−1)2+(−1)2+(−5)2+(−3)2+2+4+(−1)2+(−10)2+10+11+12+13+14+15+16

3. Calculate the sum of these squared values.

1+1+1+25+9+4+16+1+100+100+121+144+169+196+225+256

4. Simplify the sum.

1369

5. Take the square root of the sum to find the Frobenius norm.

√(,1369)=37

Final Answer

‖[1,−1,−1,−5],[−3,2,4,−1],[−10,10,11,12],[13,14,15,16]‖F=37

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