Exponential matrix calculation with the exp() function vs procedure with the use of the eigen() function

New to Julia
,
5

using r = real. (…) I can plot the result:

C=[-0.4 -1;1 0.45]
x0=[0 0.22]
∆t = .25
F=eigen(C*∆t)
v=F.vectors
Λ=exp.(F.values)
D=diagm(Λ)
r=v*D*inv(v)
T=real.(r)
x = x0
x1 =x0 
for i = 1:100
x = x*T #repeatedly multiply by T
x1=vcat(x1, x) # & store current x1(t) in the array x1
end
p1=plot( x1)
p2=plot(x1[:,1],x1[:,2])
plot(p1, p2,layout = (2, 1), legend = false)

plot_Real

how to plot the results using it using imaginary numbers?:

C=[-0.4 -1;1 0.45]
x0=[0 0.22]
∆t = .25
F=eigen(C*∆t)
v=F.vectors
Λ=exp.(F.values)
D=diagm(Λ)
r=v*D*inv(v)
x = x0
x1 =x0 
for i = 1:100
x = x*r #repeatedly multiply by T
x1=vcat(x1, x) # & store current x1(t) in the array x1
end
plot(x1)
plot(x1[:,1],x1[:,2])

plot_Real Imag

plot(x1[:,1],x1[:,2])
ERROR: MethodError: no method matching isless(::Float64, ::Complex{Float64})
Closest candidates are:
  isless(::Float64, ::Float64) at float.jl:465
  isless(::Missing, ::Any) at missing.jl:87
  isless(::AbstractFloat, ::AbstractFloat) at operators.jl:165
  ...
Stacktrace:
 [1] min(::Complex{Float64}, ::Float64) at .\operators.jl:431
 [2] expand_extrema! at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\axes.jl:335 [inlined]
 [3] expand_extrema!(::Plots.Axis, ::Array{Complex{Float64},1}) at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\axes.jl:358
 [4] expand_extrema!(::Plots.Subplot{Plots.GRBackend}, ::Dict{Symbol,Any}) at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\axes.jl:388
 [5] _expand_subplot_extrema(::Plots.Subplot{Plots.GRBackend}, ::Dict{Symbol,Any}, ::Symbol) at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\pipeline.jl:366
 [6] _process_seriesrecipe(::Plots.Plot{Plots.GRBackend}, ::Dict{Symbol,Any}) at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\pipeline.jl:402
 [7] _plot!(::Plots.Plot{Plots.GRBackend}, ::Dict{Symbol,Any}, ::Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1}}) at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\plot.jl:234
 [8] plot(::Array{Complex{Float64},1}, ::Vararg{Array{Complex{Float64},1},N} where N; kw::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\plot.jl:57
 [9] plot(::Array{Complex{Float64},1}, ::Array{Complex{Float64},1}) at C:\Users\hermesr\.julia\packages\Plots\qZHsp\src\plot.jl:51
 [10] top-level scope at REPL[154]:1