Inversion is the process of creating the opposite. Familiar examples include multiplicative inverse $2 \mapsto 1/2$, inverting functions $f(x) \mapsto f^{-1}(x)$, matrix inverse $M \mapsto M^{-1}$ etc. Please include an additional subject tag such as (linear-algebra) or (arithmetic) to help clarify ...
2
votes
2answers
69 views
calculating an inverse of a split function
I am having difficulty taking the inverse of the following function:
$$ f(x)=\begin{cases}
\frac{1}{4 \sqrt{ |1-x|}} & \text{if} \ x\in [0,2] \\
0 & \text{otherwise}\end{cases}$$
Could ...
1
vote
2answers
274 views
RYB and RGB color space conversion
I am working on a project where I need to convert colors defined in RGB (Red, Green, Blue) color space to RYB (Red Yellow Blue).
I managed to solve converting a color from RYB to RGB space based on ...
1
vote
1answer
159 views
Derivative of matrix inverse
I am trying to find the derivative of a matrix with respect to the inverse of the same matrix. The matrix in question is a non singular symmetric matrix. Any thoughts?
1
vote
1answer
62 views
inverse of function
Thanks for the help! Here is the solution..
i had a problem:
$$f(x)=\frac{(\sqrt x+8)}{(5-\sqrt x)}$$
i had to find the inverse, so lets begin...
1) first i write in terms of $y$
...
3
votes
1answer
222 views
Matrix Pseudo-Inverse using LU Decomposition?
What is the step by step numerical approach to calculate the pseudo-inverse of a matrix with M rows and N columns, using LU decomposition?
So far, I have found this, but it uses singular value ...
3
votes
3answers
173 views
Evaluate the derivative of an inverse function by using a table of values?
Given the function and derivative values in the table below, evaluate $\frac{d}{dx}f^{-1}(3)$
...
3
votes
1answer
322 views
Is the trace of inverse matrix convex?
Hi I would like to know whether the trace of the inverse of a symmetric positive definite matrix $\mathrm{trace}(S^{-1})$ is convex.
Actually I know that the trace of a symmetric positive definite ...
1
vote
1answer
344 views
Prove that if A is an invertible matrix, then A*A is Hermitian and positive definite.
If I'm not mistaken, if a matrix M has its conjugate M*=M, then M is Hermitian.
In this case then, am I asked to show that (A*A)*=A*A ? What does it have to do with A being invertible though?
And ...
2
votes
0answers
41 views
Inverse of a sub-matrix
I have a multivariate Gaussian distribution with known $\mu$ and $\Sigma$. I want to evaluate it given a vector $x$. However, some of the attributes of this vector may be unknown, in which case I want ...
0
votes
1answer
36 views
Proving the area function has an inverse
I am able to differentiate A at x using the FTC, but then I was wondering how one could show that A was one to one and prove that it has an inverse. If anybody could please help.
2
votes
1answer
57 views
Identify the equation of the normal line?
Identify the equation of the normal line to the curve $y=g(p)=2.5+3.5(4^p)$ where it crosses the $y$-axis.
So I am guessing the normal line would be the inverse of the derivative function, since it ...
1
vote
3answers
64 views
Inverse function — need help
I'm a senior software developer but my math lessons are a bit rusty. I know the name of what I want, but not anymore how to compute it ;)
I've found (by myself with Grapher.app) a simple easing ...
1
vote
2answers
668 views
Matrix is singular to working precision
I have a problem while evaluating inverse using inv in MATLAB.
My matrix looks like this:
...
3
votes
1answer
136 views
Inverse of a diagonal matrix plus a Kronecker product?
Given two matrices $X$ and $Y$, it's easy to take the inverse of their Kronecker product:
$(X\otimes Y)^{-1} = X^{-1}\otimes Y^{-1}$
Now, suppose we have some diagonal matrix $\Lambda$ (or more ...
0
votes
2answers
39 views
The inverse of $A+O(N^{-1})$
Assume $A$ is invertible and I want to calculate $(A+O(N^{-1}))^{-1}$
I want to know if there exist any formula for it?
$O(N^{-1})$ is the big $O$ notation. That is the inverse of an invertible ...
3
votes
4answers
128 views
How to show $AB^{-1}A=A$
Let $$A^{n \times n}=\begin{pmatrix} a & b &b & \dots & b \\ b & a &b & \dots & b \\ b & b & a & \dots & b \\ \vdots & \vdots & \vdots & ...
1
vote
0answers
146 views
quadratic form of trace_inverse of symmetric positive definite matrix
I have the following problem:
I need to implement a program that doesn't accept the matrix quadratic form $B^T\times B$ but it accepts the scalar quadratic form instead.
Actually I need to find a ...
5
votes
3answers
288 views
If $A$ and$ I+AB$ are invertible, show $I+BA$ is also invertible
Show that if $A$ and $I+AB$ are invertible, then $I+BA$ is also invertible with
$$(I+BA)^{-1} = A^{-1}(I+AB)^{-1}A$$
4
votes
1answer
84 views
solve $ y = (A+B^{-1})x $ for $x$
I wish to solve numerically for $x$,
$$ y = (A+B^{-1})x $$
with $A, B$ positive definite. So,
$$ x = (A+B^{-1})^{-1}y $$
I would like to avoid calculating $B^{-1}$ since that's generally bad.
...
2
votes
2answers
41 views
What is the domain of the following inverse function?
The original function is $f(x)= (3x-2)^.5$
find $y=f^{-1}(x)$ and its domain.
So I found the inverse equation to be $y=((x^2)+2)/3 $
The correct answer for the domain is all reals when $x \geq 0$. ...
0
votes
1answer
17 views
Why are the conditions of the IFT not necessary
The Inverse Function Theorem states sufficient conditions for a function to have a continuous inverse.
When, if it all, are these conditions necessary conditions? Is there a nice counterexample?
0
votes
1answer
57 views
how to inverse a matrix step by step using following example
i m making a program for hill cipher encrytion and decryption. for that i am trying to understand the logic behind it. The best example I have been given is in the following link.
...
2
votes
2answers
69 views
Inverse of inverse of function?
What is the inverse of inverse of a function (I assume the original function is invertible)? Is this the original function? Is it always true?
2
votes
3answers
263 views
The relation between an exponential function and a logarithmic function
I have been told multiple times that the logarithmic function is the inverse of the exponential function and vice versa. My question is; what are the implications of this? How can we see that they're ...
2
votes
2answers
92 views
Conditions under which $\Bbb{R}^2$ is a field.
On my assignment one of the questions asks me to prove that $\Bbb R^2$, a set containing ordered pairs of real numbers, with the operators:
$(a,b)+(c,d)=(a+c,b+d)$
$(a,b)\cdot(c,d)=(ac,bd)$
is not ...
2
votes
0answers
174 views
How to calculate the submatrix inverse with prior knowledge of matrix inverse?
Given $A\in \mathbb{N}^{n\times n}$, then $A(\mathcal{I})$ is defined by first deleting the those columns with index in $\mathcal{I}$ and then extracting the first $n-|\mathcal{I}|$ rows.
Note that ...
1
vote
1answer
56 views
Will SADMEP always work to evaluate the inverse of a function, and I should not evaluate right to left?
How do you evalulate $f^{-1}(5)$ where $f(x) = (3 + 2) - (x * 4)$
I understand that if $f(x) = y$ then $f^{-1}(y) = x$
The input and output are essentially reversed. The most common place I have ...
2
votes
1answer
42 views
Proof that an inverse of a possibly noncomputable function is possibly not decidable
I'm stuck with the following homework:
Given an fixed function $f:\mathbb{N}\to\mathbb{N}$. $f$ is an arbitrary (possibly not computable, possibly partial) function. Show that the set $\{f(42)\}$ is ...
0
votes
0answers
49 views
Zero's of the General septic equation in nonhypergeo?
Can the zero's of the general septic equation be expressed in special functions apart from the hypergeometric ones ?
We know that the zero's for the general quintic can be expressed by other ...
2
votes
0answers
30 views
Equation between the two branches of the lambert w function
Is there an equation connecting the two branches $W_0(y)$ and $W_{-1}(y)$ of the Lambert W function for $y \in (-\tfrac 1e,0)$?
For example the two square roots $r_1(y)$ and $r_2(y)$ of the equation ...
4
votes
2answers
128 views
Solve equation $\tfrac 1x (e^x-1) = \alpha$
I have the equation $\tfrac 1x (e^x-1) = \alpha$ for an positive $\alpha \in \mathbb{R}^+$ which I want to solve for $x\in \mathbb R$ (most of all I am interested in the solution $x > 0$ for ...
2
votes
4answers
149 views
is this function invertible ??
given the function
$$ f(x)= x+\cos(x)+\sin(\cos(x)) $$ (1)
is this invertible ?? i mean it exists another function $ g(x) $ so
$$ f(g(x))=x $$
my guess is that for big $ x \gg 1 $ the function ...
1
vote
2answers
85 views
What does this syntax mean: “$f^{-1} : N_{10} \Rightarrow N_b $ is the inverse of $f: N N_{b} \Rightarrow N_{10}$?”
I'm trying to solve this but I haven't seen syntax like this before. Can someone please explain the syntax?
http://i.imgur.com/GO1Ki.png
The image is
Show that the one-to-one function $f^{-1} : ...
4
votes
1answer
139 views
Inverse function notation
Suppose $f$ and $g$ are functions that fail to be one-to-one, but $f+g$ is one-to-one. Has anyone ever seen the notation $(f+g)^{-1}$ for the inverse function in that situation? (I find myself ...
1
vote
1answer
63 views
A differentiable injective function with Lipschitzian Inverse
I'm having difficulty with the following question which was given to me following studying the inverse mapping theorem.
Let $U\subseteq\mathbb{R}^{n}$
be an open set and let $f:U\to\mathbb{R}^{n}$
...
0
votes
1answer
78 views
Help with restricted domain of a function to find inverse
Restrict the domain of $f(x)$ to find inverse:
\begin{align}
f(x) & = x^2+6x+9 = (x+3)^2 \\
g(x) & = \sqrt{x} - 3
\end{align}
0
votes
2answers
434 views
To invert a Matrix, Condition number should be less than what?
I see that there is a matlab tag in this site, so I ask my question here and not in stackoverflow although it is also related to programming in matlab.
I am going to invert a positive definite matrix ...
4
votes
2answers
105 views
$\ln(x)$, $e^{x}$ and $\int \frac{1}{x}dx$ relationship
My math professor told me that $\int_1^x \frac{1}{t} dt$ is $\ln(x)$ by the definition; so far so good.
But how/why does $\ln(x)$ ($\int_1^x\frac{1}{t} dt$: by defintion) coincide with the inverse of ...
0
votes
2answers
112 views
$e^x-x-4$equating with zero
I want to find out the values of x where the $f(x) = e^x-x-4$ will equal zero.
My problem by solving this myself is that I cannot use logarithm natural (ln) because I have a normal x:
$f(x) = e^x - ...
2
votes
1answer
72 views
For square matrices $A$, $B$, is $AB=I$ sufficient that $A$ and $B$ are inverse of each other? [duplicate]
Possible Duplicate:
If $AB = I$ then $BA = I$
If $A$ and $B$ are two square matrices, and we know $AB=I$ where $I$ is the identity matrix. Is it sufficient that $BA=I$ as well so that $A$ ...
1
vote
3answers
83 views
Is this an invertible linear transformation?
Suppose you have a linear transformation $T: M_{2\times 2}\to M_{2\times 2}$ given by
$$ \begin{pmatrix} a & b \\ c & d\end{pmatrix}\mapsto \begin{pmatrix} a+b & a \\ c & ...
0
votes
1answer
33 views
Error bound for pseudoinverse
Hi I have a generic matrix A, is it possible to bound the error defined as $\|A^+A−I\|$ ??
Are there some reasonable assumptions (es. random matrix, etc...) I can make in order to have a better bound ...
0
votes
1answer
16 views
Should I check Multicollinearity When There is An Inverse?
At Machine Learning algorithms there are usually inversion process about matrices and sometimes Matlab throws error when Multicollinearity occurs.
Should I check Multicollinearity(and how) everytime ...
2
votes
1answer
104 views
Finding inverse of a function that is mixture of exponentials
How can we find the inverse of this function?
$$y=\exp(ax)+\exp(bx),$$
where $a$ and $b$ are constants
0
votes
1answer
159 views
Method of finding inverse of a Matrix using minimal polynomials
Using a piece from my last question I want to show how to find $A^{-1}$ as a polynomial expression in $A$ of degree < $\deg m_A$ where the leading coefficient of the polynomial is ...
3
votes
4answers
106 views
How do you take the multiplicative inverse of a p-adic number?
I am reading the wiki page for p-adic numbers and it states that they are a field extension of the rationals so each member has to have a modular multiplicative inverse.
So how would I take the ...
1
vote
2answers
98 views
second derivative of the inverse function
I know that the derivative of the inverse function of $f(x)$ is $g'(y) = \frac{1}{f'(x)}$
But how to derive the formula for the second derivative of g(y) knowing that $[\frac{1}{f(x)}]' = ...
2
votes
1answer
124 views
Computing inverse two-sided Laplace transform symbolically
How can I compute the inverse two-sided Laplace transform symbolically?
I know MATLAB has ilaplace[1], but that's just for a one-sided transform.
[1] ...
1
vote
2answers
360 views
Find inverse of exponential function
Do you know how I could compute the inverse function of the following exponential sentence?
$$y=\dfrac{e^x}{1+2e^x}$$
1
vote
1answer
726 views
Find inverse of polynomial function
Do you know how I could compute the inverse function of the following polynomial?
$f(x) = x^5+x^3+x$
Thanks in advance.
