Absolute Value and Matrix

[BruceTTT]

What does the absolute value do to a matrix argument? For a 2x2 identity matrix it returns the square root of 2. For [[2,0][0,2]] it returns 2 root 2.

[Paul Dale]

Frobenius norm perhaps?

Most likely one of the matrix norms.

- Pauli

[Michael de Estrada]

That's because it returns the Frobenius (Euclidean) norm of the matrix array, which is the square root of the sum of the squares of the matrix elements. So for a 2x2 identity matrix it's sqrt (1^2+1^2) = sqrt (2). In the special case of a 2D or 3D vector, the absolute value is interpreted as the magnitude or length of the vector.

Edited: 5 Nov 2013, 12:12 a.m.

[BruceTTT]

OK, thanks. Do you mean a 1D vector that || interprets as the norm? I see that [3 4] || returns 5.

Also, is there a LIST-> function?

[Michael de Estrada]

I meant a vector in 2D or 3D space, where the values are the coordinates. So it's a 1x2 or 1x3 matrix, which is commonly referred to as a vector. Regardless, it is the SRSS (square-root-of-the-sum-of-the-squares).

As to your second question I'm not sure what you are asking.

[Walter B]

Quote:

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Do you mean a 1D vector that || interprets as the norm?

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A 1xn or nx1 matrix is called a vector (of dimension n>1). FYI, a '1D vector' is a (scalar) number.

d:-)