sum of positive definite matrix $A+B $is positive definite. I want to look at the spectrum of $C=A+B$

can we say the ith largest eigenvalue of $C$ is no less than the ith largest eigenvalue of $A$ i.e. $B$ as positive definite matrix, has contribution to the growth of spectrum?

remark:

sorry my question may be too stupid, actually it is originally from

https://mathoverflow.net/questions/312946/sum-of-matrix-and-its-spectrum

and

https://mathoverflow.net/questions/312834/sum-of-gaussian-matched-by-brownian-motion

very appreciated for the help!

if "sum of matrix and its spectrum" is solved, "Sum of Gaussian matched by Brownian Motion?" would be solved.