0
votes
1answer
33 views

Subspaces and annihilators

I am trying to show this question. My understanding of annihilators is that for a vector space $V$ over $K$, with $S$ being a subset, the annihilator of $S$ is the subspace $S^0$ of linear functions ...
0
votes
3answers
54 views

Showing that two vector spaces aren't isomorphic?

Here is a part of an exercise (from a book) I can't figure out how to solve : Les $V$ be the set of all functions $f: \mathbb{N} \to \mathbb{R}$. We define also the functions $e_i(n)$ by $e_i(n)=1$ ...
1
vote
2answers
71 views

Linear functionals and dual bases

How do I tackle this question? I am a little hazy on linear functionals and integral signs.
0
votes
1answer
40 views

Matrices and bases

Can you please verify my argument: Let $M = \begin{pmatrix} a & b\\ c& d\end{pmatrix}$, where $a,b,c,d$ are all real. $$AM=\begin{pmatrix} c & d\\ a& b\end{pmatrix}$$ Let $B$ be ...
0
votes
1answer
27 views

Numerically find all zeros of multivariate function

How do I find all zeros of a multivariate function , i.e. f(x1,x2,x2,...xn)=0 numerically? I don't know exact analytic form of f , but can numerically compute f at every point on its domain. ...
4
votes
1answer
98 views

$f(AB)=f(A)f(B)$, show that $f$ is or injective or zero

Let $f\in\mathcal{L}(\mathcal{M}_n(\mathbb{R}))$ such that: $\forall(A,B)\in\mathcal{M}_n(\mathbb{R}),f(AB)=f(A)f(B)$ How can I show that $f$ is or injective or the null function ? What I have ...
1
vote
1answer
14 views

composition sum of functions/sum of composition of functions

I know it sounds really dumb, but is it true that $(f_1+f_2)\circ g=f_1\circ g+f_2\circ g$? I know it must be really elementary, but I don't recall seeing this being proved (or defined) explicitly.
1
vote
1answer
24 views

Properties determining boundedness of function

The function I am looking at is $$f(x) = \frac{1}{2}x^TAx + b^Tx + c$$ where $A$ is a symmetric matrix in $\mathbb{R}^{n\times n}$ and $b,c$ belong to $\mathbb{R}^n$ I want to determine what ...
2
votes
1answer
40 views

A question on the Wronskian

Let $f(z),g(z)$ be two complex-valued functions defined in some domain $D$. Suppose we want to show that $$f(z)+g(z)\neq 0 \tag1$$ for all $z\in D$. I think I'm right in saying we can use the ...
2
votes
1answer
143 views

Find $f$, such that $\,f,f',\dots,f^{(n-1)}\,$ linearly independent and $\,f^{(n)}=f$

I am trying to find a function $f\in\mathcal{C}^\infty(\mathbb{R},\mathbb{C})$, satisfying the differential equation $$ f^{(n)}=f, $$ and with $\,f,f',\dots,f^{(n-1)}\,$ being linearly independent. ...
0
votes
1answer
31 views

f is surjective ⇐⇒ $∀V ⊂ Y$, $f(f^−1 (V ))$ = V prove?

$f$ is surjective ⇐⇒ $∀V ⊂ Y$, $f(f^{−1} (V ))$ = $V$ This is an assertion and i said it was true. But i am confused as to what is referred to as the domain and range in this question. I would say ...
2
votes
0answers
36 views

subspace of the Vector Space of real valued functions

This is a problem from Hoffman and Kunze's Linear Algebra 2nd edition. I am trying to determine whether or not a particular subset of the set of all real valued functions is a subspace. I've done ...
-2
votes
2answers
47 views

Hey guys. Given the graph below, find the equation of the transformed parent function. [closed]

It would be great if there is a detailed explanation. Also, is there a standard method I can use to answer all kinds of graphs including exponents and logs? Thanks
0
votes
0answers
23 views

Seam Carving - Energy functions. How do they work?

I have been taking an interesting in dynamic programming and more specifically Seam Carving. For those who are not aware what this is, please look here and for some more detailed information here. If ...
0
votes
3answers
18 views

Concurrency of lines

If the three lines: $$x\sin^2 \theta + y \cos^2 \theta = 1$$ $$x \cos^2 \theta + y \sin^2 \theta = 1$$ $$lx + my + n = 0$$ are concurrent then which of the following is true? a) $l+m=n$ b) ...
1
vote
2answers
53 views

Proof - Inverse of linear function is linear

This is my first proof related to linear functions. It refers to the linear-algebra-$\textit{linear}$ (not the calculus-$\textit{linear}$). Please comment. Theorem The inverse of a linear bijection ...
-1
votes
1answer
20 views

Straight lines - point of intersection

Question: Two rays in the first quadrant: $$x +y = |a|$$ $$ax - y = 1$$ intersect each other in the interval $a \in (a_0, \infty)$, the what is the value of $a_0$? I don't even understand where to ...
4
votes
3answers
89 views

Intuitive and convincing argument that functions are vectors

Back to school time again. As I'm discussing all the mathy stuff and insights gained over the summer, I cannot help but notice that many of my peers in second or third year undergrad cannot bridge the ...
0
votes
1answer
27 views

Blend n number of values by distance

I have n number of values which each have a distance that determens how much of the amount that should be blended. I've tried to illustrate my problem visually: The blue numbers is the values, the ...
1
vote
2answers
50 views

linear function that satisfies both conditions

I am having problems understanding how to solve this question. Find a linear function that satisfies both of the given conditions. $f(-1) = 5, f(1) = 6$ Thanks, Note: i have the answer, just need ...
1
vote
1answer
26 views

Multidimensional fitting of two data sets

My problem is the following: A laser gives out a bunch of data points which are reflected off a metal surface and recorded by a camera attached to the side of the laser. The image the camera receives ...
0
votes
0answers
27 views

What happens when scaling a rectangle using a pivot point?

With multitouch screens, you can pinch to zoom. When such a gesture is triggered you are supplied with: An x scale factor; A y scale factor; A x pivot point; A y pivot point. When I have a ...
0
votes
4answers
41 views

Surjective function - proving

$f: \mathbb{R}\to \mathbb{R}$ $f(x) = x^3 -2x^4$ In order to prove that $f$ is not surjective, my teacher told me to find that in most the $f$ is negative. And indeed, only for $0<x<0.5$ it's ...
1
vote
1answer
38 views

Surjective functions and cal'

$f,g: \mathbb{R}\to \mathbb{R}$ Both are also surjective functions. My question is if $f+g$ will be also surjective. I need to dis/prove it if it's true or false. Now, my friend told me it's false ...
0
votes
0answers
29 views

Is the following subset a vector subspace of F(R,R). How to prove that it is a subspace.

Is the following subset a vector subspace of F(R, R)? The set of functions f : R → R such that f(x + 2) = f(x) for all x ∈ R I know this is obviously a subspace, but the mark scheme didn't ...
1
vote
2answers
63 views

Is a norm on $R^n$ linear?

I was reading the book Linear Algebra Done Right by Axler. In the chapter on inner product space (Ch.6), he defines the norm of x on $R^n$ space as: $||x|| = \sqrt{x_1^2 + ... + x_n^2}$ and says: ...
0
votes
1answer
22 views

Graph exponential function

I am having problems understanding why $xe^x + 10e^x$ has two $(x,y)$ intercepts. I understand why there is one $(0,10)$, but am unclear on how to return $(-10,0)$. Any help would be much ...
3
votes
1answer
82 views

Is $f(t)=(\cos(t),\sin(t))$ a function?

In the Linear Algebra book we're using (Linear Algebra with Applications, Bretscher, p.129), the author defines this as the function of the unit circle. I understand why the equation of a circle ...
1
vote
3answers
31 views

Find that the given linear transform is a isomorphism

I'm studying Linear Algebra and I'm having trouble demonstrating that a function is a isomorphism, that is: "Given the linear transform $T: V \rightarrow W$, $T$ is a isomorphism if and only if it is ...
-1
votes
1answer
29 views

Understanding a definition for vector-spaces

Let $V$, a finite dimensional vector space, and $L$, a subspace of $V$. Let $T:V^*\rightarrow L^*$ defined as: $T(\varphi)(x)=\varphi(x)$ for all $\varphi \in V^*$. Prove $T$ is onto. Well, I'm ...
1
vote
1answer
31 views

$\ker S$ is not contained in $\ker T$ implies $\dim \Im T \ge 1$

Let $T,S:V\rightarrow W$.where $V$ is a finite vector space above $F$ and $W$ is one-dimensional vector-space above $F$ ($\dim W = 1$). It is given that $\ker S$ isn't contained in $\ker T$. Why is ...
1
vote
2answers
61 views

Having trouble understanding what ker f is

I am trying to understand what exactly 'ker f' is. My guess is that it is a set of all of the elements that were lost in the process of a mapping. For example: $f:A\to B$ $f = \left\{ \begin{align} ...
0
votes
0answers
50 views

Scale invariance property of function

Consider a function $f_j$:$\mathbb{F}_p$ $\longrightarrow$ $\mathbb{F}_p$ where the set $\mathbb{F}_p$ is defined as $\{0,1,2,\dots,p-1\}$. Clearly there are $p^p$ possible maps. Here the index $j$ ...
0
votes
1answer
107 views

Difference between horizontal and vertical line tests.

Trying to understand what the differnce is between a vertical and horizontal line test. If an equation fails the vertical line test, what does that tell you about the graph? If an equation fails the ...
0
votes
0answers
51 views

Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and ...
2
votes
2answers
70 views

Constructing a function similar to x^3 between [0,1]

I'm trying to construct a function $f$, in order to normalize a dataset(obviously where all the element come from $[0,1] \in \mathbb{R}$. The big picture is that the envisioned $f: [0,1] \rightarrow ...
0
votes
1answer
36 views

Linear independence of a set of 'simple' functions

I have some $\alpha = \{f_0(x),f_1(x),\dots,f_n(x)\}$ Where having the $k$ in $f_k(x)$ equal $x$, meaning $k=x$ makes $f_k(x)=1$ or zero if $k \ne x$. Now I want to show $\alpha$ is linearly ...
7
votes
1answer
174 views

Determine an explicit expression for $f$.

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ a continuous function, bounded such that the space $\mathrm{lin}\{f_k(x)=f(x+k)∣k ∈\mathbb{N}\}$ is finite-dimensional. Determine an explicit ...
0
votes
0answers
30 views

Elementwise operations vs. matrix functions

Is there any notable connection in general case between elementwise matrix operations (such as matrix addition, scalar multiplication, Hadamard-product), and matrix functions (such as power of ...
1
vote
1answer
31 views

Kalman's controllability condition implies that the r.h.s. is “non-degenerate.”

Assume $f:\mathbb R^n\times\mathbb R\to\mathbb R^n$ is given by $f(x,u)=Ax+bu$ for some choice of coordinates $(x,u):x\in\mathbb R^n,u\in\mathbb R$, some constant matrix $A\in M_n(\mathbb R)$, and a ...
0
votes
1answer
47 views

Function Decomposition

How do I decompose a function when I'm given $f(g(x))$ and $f(x)$ and the required is $g(x)$? I done some searching on Google and most sites demonstrate the solution where it's left open, they just ...
0
votes
2answers
26 views

Construct a basis for a finite subspace of the Function Space V

Let X a non empty set, $F$ a field and $V$ the set of function of $X$ on $F$. If $f,g \in V$ and $\lambda \in F$ , $f +g ,\lambda f \in V$ are the functions such that $\forall x \in X$, ...
2
votes
2answers
96 views

Determining Whether a Function is Odd or Even from its Equation

I don't understand how this "Equation" is even being solved. I understand I have to substitute -x in for x but after that I don't know understand what's going on here. Please someone explain to me ...
1
vote
2answers
32 views

Inverse function (basic algbra math)

Consider the following function: $f(x) = {1 / (x-6) }$ Find a formula for the inverse of the function. Here is what have so far? $y = 1/(x-6)$ ---> $ x = 1/(y-6) $ But my embarrassing problem is ...
1
vote
1answer
34 views

How to write this function?

I do not want the answer given to me, I just want assistance. Problem: Marcus invests $750 in an account that pays 9.8% interest compounded annually. Write a function that describes the account ...
1
vote
0answers
28 views

Formula for calculation score based on distance

I try to write function for calculating scoring from distance in my game. I found something similar : link But I need the distance(x) to be between 0-31855000 meters and score between 0 to 1000. ...
1
vote
0answers
34 views

Is this functional linear?

I know it's trivial, but is this functional not linear? $\phi:\mathbb{R}[X]\ni p \rightarrow p(0)p \in \mathbb{R}[X]$ $$\phi(p+q)=(p+q)(0)\cdot(p+q)=(p(0)+q(0))\cdot(p+q)\ne\phi(p)+\phi(q)$$
1
vote
0answers
41 views

How to approach sketching sine and cosine graphs with transformations

Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new ...
-1
votes
1answer
68 views

Let f : X → Y and g : Y → Z be bijective mappings. Show that gf is bijective

Let f : X → Y and g : Y → Z be bijective mappings. Show that gf, the composition of f and g, is bijective. I have that since f(x)=y, and g(y)=z we get g(f(x))=g(y)=z is this enough to show gf is ...
0
votes
1answer
57 views

How to solve for $f(2)$ given $3f(x)+f(2-x) = 2x^2$?

I just came across the problem where I'm given that $3f(x)+f(2-x) = 2x^2$ and I need to find $f(2)$. I know it is simple, please help me.