40 questions linked to/from Inverse of the sum of matrices
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### harmonic mean of covariance matrices.

After writing up some math, I ended up with a term like so: $\left(A^{-1} + B^{-1}\right)^{-1}$ where $A$ and $B$ are 2 covariance matrices. 1) Can I be sure that this expression is meaningful? (i....
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### Effective way to calculate the inverse (A+kB)^-1 with k changing and A, B fixed

I have a Simulink modell where I need to calculate $(A+c_k B)^{-1}$ in every time step with $c_k$ changing each iteration. Does someone know any more effective way to do it, instead of calculating a ...
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### Real parts of diagonal elements of $(I-U)^{-1}(I+U)$ are zero?

I noticed numerically that real parts of diagonal elements of $(I-U)^{-1}(I+U)$ are zero (assuming $I-U$ is invertible), where $I$ is identity matrix and $U$ is a unitary matrix ($U^\dagger U=I$). A ...
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### How to inverse $(I + \alpha M)$ for all $\alpha$ [duplicate]

I am looking for a way to solve the following equation: $$(I + \alpha M)X=F$$ $\forall \alpha \in R$ (the real domain), with $M$ a square complex matrix without any particular properties, $I$ the ...
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### Pseudoinverse of the sum of matrices

Similarly to the question posted here Inverse of the sum of matrices but in case of non-square matrices. If I want to compute the pseudoinverse of (A+B) and matrices A,B pinv(A) is known is there a ...
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### Inverse of sum of 3 matrices

I need a way to compute the inverse of the sum of three matrices: $(A + BB^T + \beta I)^{-1}$ where $I$ is identity and $\beta$ is a constant. I am not very familiar with linear algebra, but a ...
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### Convexity of a function over matrices [duplicate]

How to show that $f(X)=tr(X^{-1})$ is convex over the set of symmetric real positive definite matrices by showing that $g(t)=f(X+tV)$ is convex for any such $X$ and $V$? Clearly we need to show that ...
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