Find the Norm

Problem

‖[5,1,2,8,4,3,8,1],[5,9,1,5,7,2,9,1],[7,6,1,8,3,1,8,2],[0,5,0,8,5,4,6,7],[2,8,6,4,1,5,2,1],[0,0,0,0,0,0,0,0]‖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 in the matrix.

5,1,2,8,4,3,8,1⇒25,1,4,64,16,9,64,1

5,9,1,5,7,2,9,1⇒25,81,1,25,49,4,81,1

7,6,1,8,3,1,8,2⇒49,36,1,64,9,1,64,4

0,5,0,8,5,4,6,7⇒0,25,0,64,25,16,36,49

2,8,6,4,1,5,2,1⇒4,64,36,16,1,25,4,1

3. Sum the squared values for each row.

Row 1 sum=25+1+4+64+16+9+64+1=184

Row 2 sum=25+81+1+25+49+4+81+1=267

Row 3 sum=49+36+1+64+9+1+64+4=228

Row 4 sum=0+25+0+64+25+16+36+49=215

Row 5 sum=4+64+36+16+1+25+4+1=151

Row 6 sum=0

4. Calculate the total sum of all squared elements.

Total Sum=184+267+228+215+151+0=1045

5. Take the square root of the total sum to find the Frobenius norm.

√(,1045)≈32.32646

Final Answer

‖[5,1,2,8,4,3,8,1],[5,9,1,5,7,2,9,1],[7,6,1,8,3,1,8,2],[0,5,0,8,5,4,6,7],[2,8,6,4,1,5,2,1],[0,0,0,0,0,0,0,0]‖F=√(,1045)

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