# Questions tagged [matrix-equations]

Equations whose unknown is a matrix, such as, for instance, algebraic Riccati equations $XAX+XB+CX+D=0$ or matrix differential equations (e.g. $\dot X(t)=AX(t)$. This tag is *not* meant for general systems of linear equations $Ax=b$.

**5**

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### System of quadratic equations

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### Optimization problem on trace of complex matrix product

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### Proving that a system of polynomial matrix equations over $\mathbb{F_2}$ has no solution

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### Is the solution to the Fredholm integral equation of the first kind a continuous analogue of Cramer's rule for matrix equations?

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### System of matrix equations

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### Matrix equation involving quadratic form

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### Stability of matrix equation

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### What is the solution of the matrix equation $A X + X A' + B X B' + C = 0$ for $X$?

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### Norm of vector components optimization of linear matrix combination

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### Solving two quadratic matrix equations [closed]

**3**

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### A problem about determinant and matrix

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**1**answer

### State-dependent positive definite matrix

**1**

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### How do you solve this quadratic matrix equation?

**25**

**1**answer

### Integer matrices which are not a power

**0**

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### The relation between unit quaternions and the virtual rotation of an angular velocity vector?

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### Solving a Lyapunov inequality with a fixed block

**1**

**1**answer

### Determine unknown matrix function of particular form from known points

**2**

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### Is there a method to solve a non-linear quadratic matrix equation?

**2**

**1**answer

### Number of 5x5 matrix permutations without repetitions in rows or columns

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### Approximation bounds for matrix multiplication

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### An otherwise linear matrix equation with the presence of a signum function : reference request

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### Multiplication of matrix-represented polynomials

**1**

**1**answer

### Global polynomial basis for the kernel of a matrix polynomial

**1**

**2**answers

### Rank of a linear combination of linear operators

**2**

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### How to find the similarity transformation of a matrix operator?

**4**

**3**answers

### Properties of matrix $X=\left[\frac{1}{1-\bar\alpha_i \alpha_j}\right]_{ij}$

**1**

**1**answer

### Asymptotic behavior of a matrix equation and its eigenvalues

**6**

**1**answer

### How to obtain matrix from summation inverse equation

**7**

**1**answer

### Closed form solution for $XAX^{T}=B$

**0**

**2**answers

### Asymptotic expansion involving a matrix equation

**0**

**1**answer

### Solution for $AX+XA^T+XBX=C $ where $X$, $B$ and $C$ are symmetric

**4**

**1**answer

### Solving equation of matrix valued functions

**2**

**3**answers

### Efficient algorithm for matrix equation $AXB + BXA = F$

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### Solution to the matrix equation AX=XB in the form of generalized inverses

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### Example for diagonal Lyapunov equation with orthogonal matrix

**1**

**5**answers

### Solution for $Xa + X^Tb = c$ where $X^TX = I$? [closed]

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### A real system of bilinear equations with $2n$ unknown and equations

**1**

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### Nonlinear fixed-point equation with linear solutions?

**4**

**2**answers

### Is there any general reference on matrix quadratic equations?

**13**

**1**answer

### Necessary conditions for the existence of solution of Sylvester equation AX=XB

**3**

**2**answers

### Diagonal Lyapunov equation with rank 1

**2**

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### Matrix factorization for dimensional reduction similar to spectral decomposition/SVD

**3**

**1**answer

### Conditions for a certain matrix equation to have a full rank solution

**2**

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### Distance between two algebraic sets

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### Solving the inverse of a matrix under a uniform distribution

**1**

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### solving a non-linear Matrix equation

**2**

**1**answer

### How to solve a quadratic matrix equation with positive semidefinite constraint?

**1**

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### find a PSD matrix that that verify matrices sum of equality

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### How can I solve an orthogonal-constrained Sylvester equation?

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