Find the Norm

Problem

‖[1,2,5,9],[11,14,19,5],[7,1,3,6],[13,17,21,0]‖

Solution

1. Identify the type of norm to be calculated. In the context of matrices without a specific subscript, the Frobenius norm is the standard default, calculated as the square root of the sum of the squares of all elements.

2. Square each individual element of the matrix.

1=1

2=4

5=25

9=81

11=121

14=196

19=361

5=25

7=49

1=1

3=9

6=36

13=169

17=289

21=441

0=0

3. Sum all the squared values together.

1+4+25+81+121+196+361+25+49+1+9+36+169+289+441+0=1808

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

√(,1808)=√(,16⋅113)=4√(,113)

Final Answer

‖[1,2,5,9],[11,14,19,5],[7,1,3,6],[13,17,21,0]‖F=4√(,113)

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