Find the Norm [[4,5,-5,-3],[2,7,4,-3]]

Problem

‖[4,5,−5,−3],[2,7,4,−3]‖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 elements.

2. Square each individual element of the matrix.

4=16

5=25

(−5)2=25

(−3)2=9

2=4

7=49

4=16

(−3)2=9

3. Sum all the squared values together.

16+25+25+9+4+49+16+9=153

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

√(,153)

5. Simplify the radical by factoring out perfect squares.

√(,9⋅17)=3√(,17)

Final Answer

‖[4,5,−5,−3],[2,7,4,−3]‖F=3√(,17)

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