Normalize each column of a matrix

I have one doubt that, suppose if a matrix has zero mean and unit variance, then whether each of its columns has zero mean and unit variance or not..?

[Jan]

What is the "mean" of a matrix exactly? I do not think that this is mathematically defined.

[Berbia]

B = mean2(A)

here B is the "mean" value of matrix A.

My question is suppose if B is 0, then whether mean(A) gives a row vector of all values 0.

Answer 1

[Matt J]

No. Take the matrix

 A=[1 -1; 1 -1]

Clearly A(:) has zero mean and unit variance, but its columns individually do not.