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2 matrix norm changed by vector norm

# Ease of calculation of matrix norm

I have SPD matrix A and two vectors z and b.

Is there exist a matrix norm where I can calculate $||A^{1/2}b-z||$ without having to calculate $A^{1/2}b$ explicitly ?

1

# Ease of calculation of matrix norm

I have SPD matrix A and two vectors z and b.

Is there exist a matrix norm where I can calculate $||A^{1/2}b-z||$ without having to calculate $A^{1/2}b$ explicitly ?