[College Level] Norm of Matrices

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SUMMARY

The discussion centers on the definition and calculation of matrix norms, specifically addressing confusion around the formula for the norm of a matrix. The example matrix provided is [[1, 3], [0, 1]], leading to the calculation of the norm as Sqrt((11 + sqrt(117))/2). The participants clarify that the norm is derived from the square root of the sum of the squares of the matrix entries, not merely the square root of the entries themselves. The conversation emphasizes the need for precise definitions and understanding of matrix norms, as outlined in resources like the Wikipedia page on matrix norms.

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Th3HoopMan
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So I'm studying norm of matrices in my calc class, and most resources I've looked at seem like it's just the square root of all the entry values over the sum of all the entries, but when given the matrix

[1 3]
[0 1]

Sqrt((11+sqrt(117))/2)

The 11 is the sqrt of 12 + 32 + 12

the 2 is the root of 1 + 3 + 1, where does the plus sqrt(117) come from?
 
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Um...

1^2 + 3^2 + 1^2 is 11. In what sense is 11 the square root of that?

1 + 3 + 1 is 5. In what sense is 2 the square root of that?

Can you possibly re-state the definition of the norm you are using? The phrase "the square root of all the entry values" does not make sense. Do you mean, the square root of the sum of the squares of the matrix values?

http://en.wikipedia.org/wiki/Matrix_norm

Which matrix norm do you think you are using?
 
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