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

Problem

‖[1,2,1],[1,2,1]‖

Solution

1. Identify the type of norm to be calculated. For a matrix A the default norm is typically the Frobenius norm, denoted as ∥A∥

2. Apply the formula for the Frobenius norm, which is the square root of the sum of the squares of all elements in the matrix.

∥A∥=√(,(∑_i=1^m)((∑_j=1^n)(|))*(a_i*j)|2)

3. Square each individual element of the matrix.

1=1

2=4

1=1

1=1

2=4

1=1

4. Sum the squared values together.

1+4+1+1+4+1=12

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

√(,12)=√(,4⋅3)=2√(,3)

Final Answer

‖[1,2,1],[1,2,1]‖F=2√(,3)

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