Find the Norm [[1,-1,2,3],[0,1,4,3],[1,0,3,5]]

Problem

‖[1,−1,2,3],[0,1,4,3],[1,0,3,5]‖

Solution

1. Identify the type of norm to be calculated. Since no specific norm was requested, the Frobenius norm (the square root of the sum of the squares of all elements) is the standard calculation for a matrix.

2. Square every individual element in the matrix.

1^2+(−1)^2+2^2+3^2+0^2+1^2+4^2+3^2+1^2+0^2+3^2+5^2

3. Sum the squared values.

1+1+4+9+0+1+16+9+1+0+9+25=76

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

√(,76)

5. Simplify the radical expression.

√(,4⋅19)=2√(,19)

Final Answer

‖[1,−1,2,3],[0,1,4,3],[1,0,3,5]‖_F=2√(,19)

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