Find the Norm

Problem

‖[0,0,0,−1],[0,1,−1,3],[0,0,1,2],[1,7,4,−4]‖

Solution

1. Identify the type of norm to be calculated. Since no specific norm was requested, the standard Frobenius norm (the Euclidean norm of the matrix) is typically used.

2. Square every individual element in the matrix.

0+0+0+(−1)2+0+1+(−1)2+3+0+0+1+2+1+7+4+(−4)2

3. Sum the squared values.

0+0+0+1+0+1+1+9+0+0+1+4+1+49+16+16

4. Simplify the sum.

1+1+1+9+1+4+1+49+16+16=99

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

√(,99)=√(,9⋅11)=3√(,11)

Final Answer

‖[0,0,0,−1],[0,1,−1,3],[0,0,1,2],[1,7,4,−4]‖F=3√(,11)

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