Find the Norm [[2,6],[-4,-12]]

Problem

‖[2,6],[−4,−12]‖

Solution

1. Identify the type of norm to be calculated. In the absence of a specific subscript, the Frobenius norm (the Euclidean norm of the matrix) is the standard interpretation for a matrix norm.

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.

3. Square each individual element of the matrix.

2=4

6=36

(−4)2=16

(−12)2=144

4. Sum the squared values together.

4+36+16+144=200

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

√(,200)=√(,100⋅2)=10√(,2)

Final Answer

‖[2,6],[−4,−12]‖=10√(,2)

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