Find the Norm [[3,2,1],[5,3,2]]

Problem

‖[3,2,1],[5,3,2]‖F

Solution

1. Identify the type of norm to be calculated. For a matrix, the default norm is typically the Frobenius norm, which is the square root of the sum of the squares of all its elements.

2. Square each individual element of the matrix.

3=9

2=4

1=1

5=25

3=9

2=4

3. Sum all the squared values together.

9+4+1+25+9+4=52

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

√(,52)

5. Simplify the radical expression by factoring out the largest perfect square.

√(,4⋅13)=2√(,13)

Final Answer

‖[3,2,1],[5,3,2]‖F=2√(,13)

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