Eigenvectors and Eigenvalues explained visually


284 bookmarks. First posted by gregonicus january 2015.


Eigenvectors and Eigenvalues explained visually via Instapaper https://ift.tt/1ymXdmx
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may 2018 by ejmurray72
Back Explained Visually Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank…
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may 2018 by toph
Back Eigenvectors and Eigenvalues Explained Visually Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and…
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january 2017 by Blubser
It turns out that a matrix like $A$, whose entries are positive and whose columns add up to one (try it!), is called a Markov matrix, and it always has $\lambda = 1$ as its largest eigenvalue. That means there's a value of $v_t$ for which $Av_t =\lambda v_t = 1 v_t = v_t$. via Pocket
learn  statistics  vectors 
november 2016 by kintopp
Eigenvectors and Eigenvalues explained visually via
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october 2016 by aleksshulman
Eigenvectors and Eigenvalues
Explained Visually
linear-algebra  visualization 
september 2016 by sevas
Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank algorithm. Let's see if visualization can make these ideas more intuitive.
@Article  @Concept  @CourseOutline  @Example  Math  SensoryStimulus  MeaningManagement  Tutorial 
september 2016 by jslu
Fibonacci Sequence
Suppose you have some amoebas in a petri dish. Every minute, all adult amoebas produce one child amoeba, and all child amoebas grow into adults (Note: this is not really how amoebas reproduce.). So if t
t
is a minute, the equation of this system is

adultst+1childrent+1==adultst+childrentadultst
adults
t
1
adults
t
children
t
children
t
1
adults
t
which we can rewrite in matrix form like

vt+1(adultst+1childrent+1)==A(1110)⋅⋅vt(adultstchildrent)
v
t
1
A
v
t
adults
t
1
children
t
1
1 1
1 0
adults
t
children
t
Below, press "Forward" to step ahead a minute. The total population is the Fibonacci Sequence.

children
adults
0
1
2
0
1
2
v₀
children
adults
reset forward

1 child + 0 adults = 1
1
1
2
3
5
8
13
21
34
55
89
144
233
As you can see, the system goes toward the grey line, which is an eigenspace with λ=(1+5√)/2>1
λ
1
5
2
1
.

Steady States
Suppose that, every year, a fraction p
p
of New Yorkers move to California and a fraction q
q
of Californians move to New York. Drag the circles to decide these fractions and the number starting in each state.
september 2016 by tkreagan
I think this is actually a lot more interesting for the interactive parts than it is for the linear algebra.
Math  Visualization 
september 2016 by jonchambers
Eigenvectors and Eigenvalues explained visually Back Eigenvectors and Eigenvalues Explained Visually Eigenvalues/vectors are instrumental to understanding…
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september 2016 by kishba
Interact ⇨💡 “Eigenvectors & Eigenvalues explained visually” via cc
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august 2016 by mawif
Back Explained Visually Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank…
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august 2016 by tjames
Interesting visualization of eigenvectors and eigenvalues
math 
april 2016 by jswanljung