# Tag Info

Accepted

### Exponeintal of symmetric triangular matrix

Given that your matrix is symmetric and real (we can factor by a), it can be diagonalized. Once diagonalized it'll be much easier to compute the exponential: \exp(P^T diag(\lambda_1, \cdots, \...
• 58

### Eigendecomposition of a real, symmetric matrix with distinct and nondistinct eigenvalue

This is equivalent to understanding how unique an orthonormal basis of eigenvectors for $A$ is. The answer is the following: if we write $V_{\lambda} = \ker(A - \lambda)$ for the eigenspaces of $V$, ...
• 437k
Accepted

### Decompose a $3 \times 3$ orthogonal matrix into a product of rotation and reflection matrices

Once the three eigenvalues $\lambda_i$ and associated eigenvectors $\vec x_i$ of $Q$ are computed, there are two complex-conjugated eigenvalues $e^{\pm i \phi}$ where $\phi$ is the rotation angle, and ...
• 3,458
1 vote

• 5,854
1 vote

### Decompose a $3 \times 3$ orthogonal matrix into a product of rotation and reflection matrices

The answer below is based on Jyrki Lahtonen's comment, this paper on Euler angles, and these lecture notes on rotation matrices. $\newcommand{\atant}{\text{atan2}}\newcommand{\tr}{\text{Tr }}$ If \$\...

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