Return to Question

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 if it could be solved!

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

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.

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 if it could be solved!

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 if it could be solved!

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

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?

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 if it could be solved!