Linked Questions

9
votes
3answers
2k views

Should a linear function always fix the origin? [duplicate]

I became very confused about linear functions after reading this question What is the difference between linear and affine function In the comments it says that $F(x)=2*x+4$ is NOT a linear function ...
22
votes
2answers
2k views

Why are linear functions linear?

I always thought linear functions need to satisfy $$f(x+y)=f(x)+f(y).$$ I am a tad confused now, consider $f(x)=2x+3$. $f(1)=5$, $f(2)=7$, $f(1+2)=f(3)=9 \neq f(1)+f(2)$ which was what I thought ...
2
votes
3answers
5k views

what is the difference between linear transformation and affine transformation?

Recently, I am struglling with the difference between linear transformation and affine transformation. Are they the same ? I found an interesting question on the difference between the functions. But ...
6
votes
2answers
5k views

How to prove that a function is affine?

I am trying to understand the concept of affinity of functions. First, I thought that every affine function has to be a linear function, too, because my teacher's notes define linear and affine ...
9
votes
1answer
1k views

“If $f$ is a linear function of the form $f(x)=mx+b$, then $f(u+v)=f(u)+f(v).$” True or false?

The rest of the question states the following: "If true, give an explanation as to why. If false, give a counter example." Here is the following statement: If $f$ is a linear function of ...
1
vote
2answers
5k views

New Temperature Scale

A new temperature scale is to be sued where freezing and boiling temperature of water is at -100 deg N and 100 deg N respectively. Calculate Absolute Zero in Degree N Answer is -992.6 Degree N ...
1
vote
1answer
336 views

Why is $y=f(a)+f'(a)(x-a)$ linear?

I'm reading this book: Functions of Several Variables and I didn't understand why this function is linear: I think the authors made a mistake.
2
votes
2answers
45 views

Mapping values in the range [-1, 1] to [0, 1] in an invertible fashion

I have a continuous variable whose range is within $[-1, 1]$. I want to map the values of this variable to the range $[0, 1]$ instead. What I do is I add the value of $1$ to the the variable and ...
0
votes
1answer
179 views

Linear map and affine map definition coincides?

I'm reading through a geometry proof that claims that every affine map $f:\mathbb{R}^n\to\mathbb{R}^n$ is the composition of a linear map and a translation. More precisely, $f$ is affine if and only ...
2
votes
1answer
157 views

Linear algebra, affine space, and floor function

My question is mostly: is there a name for this kind of things. I am mostly interested by finding book or articles about what follows, but without even a word or a name, it is quite hard to search for ...
0
votes
1answer
55 views

Linearity for Translations by 0?

I came across the following question, and wanted to see whether my answer was correct. Let $T_u : V \to V$ be the translation by a vector $u$. For which vectors $u$ is $T_u$ a linear map? My ...
1
vote
0answers
24 views

Families of step-wise canonical transformations.

Do there exist "families" of step-wise canonical transformations, in the sense that: $${\bf A = TCT}^{-1}, \\{\bf T = T_2}^n$$ So that $${\bf T_2}^k {\bf C} {\bf T_2}^{-k} $$ Also has some canonical ...