Related to Frobenius norm

Hello all, I am trying to find Frobenius norm of each column of 2 X 500 matrix in MATLAB but not getting it correctly.

Any help in this regard will be highly appreciated.

Answer 1

[Torsten]

From the documentation:

n = norm(X,"fro") returns the Frobenius norm of matrix or array X.

[chaaru datta]

Thank u sir for the answer...but I want to find the norm of each column of X.

[Torsten]

rng("default")
X = rand(3);
n = arrayfun(@(i)norm(X(:,i),"fro"),1:size(X,2))

n = 1×3

1.2249 1.1152 1.1373

n = vecnorm(X,2)

n = 1×3

1.2249 1.1152 1.1373

[Dyuman Joshi]

Since frobenius norm is defined as the square root of sum of the absolute squares of elements of an array, simply calculate it directly for each column -

y = rand(2,500);
sqrt(sum(abs(y).^2))

ans = 1×500

1.0265 0.8084 1.1542 0.5197 0.5827 1.0240 0.0890 1.3322 1.0956 0.4976 0.7836 0.1435 0.3630 0.7378 0.7803 1.0122 0.8657 0.8241 1.1077 0.2674 0.5666 0.6570 0.2569 0.8938 0.3199 1.0291 0.7741 0.4520 0.2461 1.0370

or use vecnorm -

vecnorm(y,2)

ans = 1×500

1.0265 0.8084 1.1542 0.5197 0.5827 1.0240 0.0890 1.3322 1.0956 0.4976 0.7836 0.1435 0.3630 0.7378 0.7803 1.0122 0.8657 0.8241 1.1077 0.2674 0.5666 0.6570 0.2569 0.8938 0.3199 1.0291 0.7741 0.4520 0.2461 1.0370

[Torsten]

@Dyuman Joshi

"abs" seems to be superfluous.

[Dyuman Joshi]

It might be, but that's how Wikipedia and Wolfram Alpha define it.

Idk why though.

[Torsten]

For complex matrices most probably.

[Dyuman Joshi]

That should be it.

For someone who has worked with real valued data only, it easily escapes my mind that people work with non-real valued data as well.