In [1]:
## LU Factorizations in Julia.
A = randn(1000, 1000)
b = randn(1000)
println("First time: ")
@time x = A\b
println("Second time: ")
@time x = A\b ; # don't display 

First time: 
  0.823344 seconds (3.17 M allocations: 168.208 MiB, 3.97% gc time, 98.06% compilation time)
Second time: 
  0.027692 seconds (9 allocations: 7.645 MiB, 49.21% gc time)
In [2]:
## If we want to save the factorization, we can do this with lufact 
println("Factorization time: ")
@time F = lu(A)
println("Solve time: ")
@time x = F\b
println("Solve time again: ")
@time x = F\b ; # don't display

Factorization time: 

UndefVarError: `lu` not defined in `Main`
Suggestion: check for spelling errors or missing imports.
Hint: a global variable of this name may be made accessible by importing LinearAlgebra in the current active module Main

Stacktrace:
 [1] macro expansion
   @ ./timing.jl:581 [inlined]
 [2] top-level scope
   @ ./In[2]:3
In [3]:
##
F.L
F.U
F.p

UndefVarError: `F` not defined in `Main`
Suggestion: check for spelling errors or missing imports.

Stacktrace:
 [1] top-level scope
   @ In[3]:2
In [4]:
## 
size(F)

UndefVarError: `F` not defined in `Main`
Suggestion: check for spelling errors or missing imports.

Stacktrace:
 [1] top-level scope
   @ In[4]:2
In [5]:
##
# This still fails... 
F = qr(randn(1000000,1)) # take the QR of a tall skinny matrix

UndefVarError: `qr` not defined in `Main`
Suggestion: check for spelling errors or missing imports.
Hint: a global variable of this name may be made accessible by importing LinearAlgebra in the current active module Main

Stacktrace:
 [1] top-level scope
   @ In[5]:3