How to do a Taylor expansion with a matrix

I have tried the official matlab website that describes the Taylor expansion, but it doesn't work!

G = [0,4;4,0];

T = taylor(exp(G));

error message "Function 'taylor' (input argument of type 'double') is undefined."

I would like to know the result of infinite convergence separately.

I would be glad if you could tell me!

[Ashutosh]

I am not sure I understand your query. A Taylor expansion can be constructed for a function of some variable x. What you are feeding into the Taylor function taylor(), seems to be a constant. You can't have a Taylor expansion, approximation or anything for a constant.

[kuroshiba]

I see, I had mistakenly thought that Taylor expansion could be done with constants!

Thanks for your comments pointing that out!

Answer 1

[Torsten]

Maybe you mean:

G = [0,4;4,0];
Gexp = expm(G)

Gexp = 2×2

27.3082 27.2899 27.2899 27.3082

or

syms t
G = [0,4;4,0]*t;
Gexp = simplify(taylor(expm(G),t,'ExpansionPoint',1))

Gexp = 

Gexp = simplify(subs(expm(G),t,1))

Gexp = 

[kuroshiba]

That is what I wanted to know! Thank you!

I'm sorry for the lack of words and understanding that bothered you.

Answer 2

[KSSV]

syms x 
f = exp(x)

f = 

T = taylor(f)

T = 

In place of x substitue each value of G.

Answer 3

[John D'Errico]

You cannot compute the Taylor series of a constant. You CAN compute a Taylor series, and then evaluate it at that constant value, since the truncated series is then a polynomial.

Will only a few terms from that Taylor series be close to yielding a convergent result? This is something you need to consider, and that is a big part of your homework where you have shown no effort. The eigenvalues of G will be an important factor.

G = [0,4;4,0];
eig(G)

ans = 2×1

-4 4

So, given that, will a simple Taylor series for exp(x) converge well for x==4 (or x==-4, for that matter)? How many terms would you expect that to require? Why did I compute the eigenvalues of G here? How are they pertinent?

[Paul]

Isn't the Taylor series of function that's a constant just the constant?

syms f(x)
f(x) = sym(8);
taylor(f(x))

ans = 

8