All Questions
4
questions
2
votes
1
answer
149
views
Extremely complex vector-matrix expression and its differentiation by vector
Given:
$Q=R_z(\psi)R_y(\xi)R_x(\phi)$ - rotation matrix
$\boldsymbol{\theta}=\left[\begin{array}{@{}c@{}} \phi \\ \xi \\ \psi
\end{array} \right]$ - vector of angles
$p=Q\left[\begin{array}{@{}...
- 731
0
votes
1
answer
34
views
Matrix differential equation set to zero
I have a bijective continuous function $f$, which maps an $(n\times1)$ dimensional column vector $t=[t_1,...t_n]'$ to another $(n\times1)$ dimensional column vector $f(t)=[f_1(t),...f_n(t)]'$. I ...
- 766
0
votes
1
answer
78
views
Inverse for a sum of two matrices
What is the inverse of the 3x3 matrix
$(\vec{a} \vec{a}+cI)^{-1}$
Where $\vec{a} \vec{a} $ is a dyad and $I$ is the identity matrix, $c$ is constant, $\vec{a}=(a_1,a_2,a_3)$ is a 3x1 vector
$\vec{a}...
- 23
2
votes
1
answer
84
views
Show that $(T_{ij})=\begin{pmatrix} \alpha &\omega &0\\-\omega & \alpha &0\\ 0 &0& \beta \end{pmatrix}$
A tensor has components $T_{ij}$ with respect to Cartesian coordinates
$x$. If the tensor is invariant under arbitrary rotations around the
$x_3$-axis, show that it must have the form $$(T_{ij})=...
- 1,639