Find the Norm

Problem

‖[1,0,0,0,−8],[0,2,0,0,0],[−2,0,4,0,4],[0,−12,0,8,−8]‖

Solution

1. Identify the type of norm to be calculated. Since the specific norm was not specified, the Frobenius norm (the square root of the sum of the squares of all elements) is the standard calculation for a matrix.

2. Square each individual element of the matrix.

1=1

0=0

0=0

0=0

(−8)2=64

0=0

2=4

0=0

0=0

0=0

(−2)2=4

0=0

4=16

0=0

4=16

0=0

(−12)2=144

0=0

8=64

(−8)2=64

3. Sum all the squared values together.

S=1+0+0+0+64+0+4+0+0+0+4+0+16+0+16+0+144+0+64+64

S=377

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

∥A∥=√(,377)

Final Answer

‖[1,0,0,0,−8],[0,2,0,0,0],[−2,0,4,0,4],[0,−12,0,8,−8]‖F=√(,377)

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