Tagged Questions
10
votes
2answers
232 views
A matrix w/integer eigenvalues and trigonometric identity
Any intuition and/or rigorous arguments on the proofs of the following statements would be appreciated:
Let $n$ be a natural number.
(a) Consider the following Toeplitz/circulant symmetric matrix:
...
1
vote
3answers
76 views
Order of operations in rotation matrix notation.
I'm trying to convert this equation to C# but I'm not a mathematician and I find math notation ambiguous:
See the first matrix in this article:
http://mathworld.wolfram.com/RotationMatrix.html
...
1
vote
2answers
78 views
Use a matrix or equations to find the value of $\sin(\pi/3)$
I was asked to use $\sin(0)=0$, $\sin(\pi/2)=1$, and $\sin(\pi)=0$ to calculate the value of $\sin(\pi/3)$ using matrices or equations. I honestly have no idea how to solve this.
-1
votes
3answers
51 views
matrix representation of a trigonometric rotation
Hey guys!I have a couple of doubts regarding this exercise, for a) I think that the Matrix
rotation of P is [(cos t, -sen t) , (-sen t, cos t)] and for Q [(-cos t, -sen t), ( sen t,
cos t)] , is ...
2
votes
4answers
228 views
How to find the exact value of $ \cos(36^{\circ}) $?
The problem reads as follows:
Noting that $t=\frac{\pi}{5}$ satisfies $3t=\pi-2t$, find the exact value of
$$\cos(36^{\circ})$$
it says that you may find useful the following identities:
...
1
vote
1answer
97 views
Rotating a line segment in 3D to a prescribed orientation
I have a general line segment with endpoints $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ referenced to a 3D Cartesian coordinate frame E. I wish to rotate this coordinate fram E to a new coordinate system F ...
0
votes
1answer
60 views
Vector Math and Directional Vectors
Short and sweet.
How does one calculate a directional vector in 3 dimensions by knowing the magnitude of the vector and the rotations about both the x and y axis?
1
vote
1answer
511 views
Angle Between Pair of Vectors
Find the angle $\theta$ between the pair of vectors u and v.
$u = \begin{bmatrix}
1\\
1
\end{bmatrix}, v = \begin{bmatrix}
7\\
11
\end{bmatrix}$
I already figured that I'll need the ...
0
votes
2answers
581 views
Linear Algebra - Linear Transformations
Let $V$ be the space spanned by the two functions $\cos(t)$ and $\sin(t)$. Find the matrix $A$ of the linear transformation $T(f(t)) = f''(t) + 7f'(t) + 4f(t)$ from $V$ into itself with ...
0
votes
1answer
492 views
Finding the position of a point after rotation: Why is my result incorrect
I am attempting to calculate the position of a point after it has been rotated
I have been using an algorithm but I am getting incorrect values which makes me think I am using the incorrect algorithm ...
1
vote
1answer
350 views
Find 3D rotation vector and angle to transform a rectangle into a given quadrilateral
I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection.
...
14
votes
5answers
946 views
$\sin(A)$, where $A$ is a matrix
If $A$ is an $n\times n$ matrix with elements $a_{ij}$ $i=$i'th row, $j=$j'th column. Then $e^A$ is also a matrix as can be seen by expanding it in a power series.Is $e^A$ always convergent and ...
2
votes
2answers
209 views
Equality of matrix of trigonometric functions in n-power
Could you help me please and give some tips on how should I start solving this problem. How can one prove, that this equation is right, when n from $\mathbb{Z}$ and $\alpha$ is from $\mathbb{R}$?
...
1
vote
1answer
300 views
Solving an equation with trig functions and two different angles
I am trying to solve this equation derived from matrix multiplication (where $a,b,c,d$ are constants):
$$-a \cos(\theta) \sin(\alpha)-b\sin(\theta) ...
3
votes
3answers
412 views
How to create 2x2 matrix to rotate vector to right side?
I have vector u=(x,y) and i need to create matrix M: M*u=(1,0).
But that matrix has to rotate vector, instead of keep and ...
7
votes
2answers
472 views
Algebraic proof of a trig matrix identity?
I'll put the question first, and then the background, because I'm not sure that the background is necessary to answer the question:
I have a geometric proof, but is there an elegant algebraic proof ...
14
votes
4answers
570 views
How does multiplying by trigonometric functions in a matrix transform the matrix?
I found this comic:
But I can't understand the humor because I can't understand how trig functions affect matrix multiplication. Can someone please explain?
0
votes
0answers
1k views
Compute Altitude and Azimuth using either Quaternions or Rotation Matrix or Roll, Pitch and Yaw component
I am struck with a mathematical problem. I want to convert the iPhone device's attitude information which is available in one of the following forms:
Quaternion
Rotation Matrix
Roll, Pitch and Yaw ...
