2
votes
2answers
105 views

How to calculate the determinant of this matrix $A=\begin{bmatrix} \sin x & \cos^2x & 1 \\ \sin x & \cos x & 0 \\ \sin x & 1 & 1 \end{bmatrix}$

How to calculate the determinant of this matrix $A=\begin{bmatrix} \sin x & \cos^2x & 1 \\ \sin x & \cos x & 0 \\ \sin x & 1 & 1 \end{bmatrix}$ ...
1
vote
1answer
70 views

Question about the matrix representation of the differentiation map on the subspace generated by $\{1, t, e^{t}, e^{2t}\}$

As mentioned in a previous post (I think), I've been trying to learn some linear algebra, and so I've begun to post little questions whose answers I'm sure are obvious to most here; this is just a way ...
3
votes
1answer
204 views

The Principle of Mathematical Induction

The question is Let $( F_0, F_1, F_2,... )$ be the Fibonacci sequence defined by $F_0=0,\, F_1=1, and F_{n+1}=F_n+F_{n-1}$, n greater than or equal to 1. Prove the following identities. ...
8
votes
2answers
233 views

Solving matrix equations of the form $X = AXA^T + C$

I'm trying to solve this matrix equation: $$X = AXA^T + C$$ In particular, $$ X = \begin{bmatrix} 1.5 & 1 \\ -0.7 & 0 \end{bmatrix} X \begin{bmatrix} 1.5 & -0.7 \\ 1 & 0 ...
0
votes
1answer
89 views

Solving a one line matrix, constraining the coefficients

I will give a simple example of my question then the full one. Let's say I am trying to reconcile my bank account, and have no statement. I opened it with $0 exactly, and a small number of ...
1
vote
0answers
56 views

Minimization of matrix of vectors in polar field

The problem I am facing is the reduction of vibrations of a rotating object. I have a series of vibration measurements taken at 5 different states with magnitude and phase components, and a set of ...
3
votes
4answers
613 views

Solving For A Linear Operator

I'm currently learning about linear operators, and the chapter in my book describing them only has examples with predefined linear operators. One of the first questions asks: ...