With the new features added to the Student[LinearAlgebra] package I wanted to go over some of the basics on how someone can do Linear Algebra in Maple without require them to do any programming.  I was recently asked about this and thought that the information may be useful to others.
 

This post will be focussed towards new Maple users. I hope that this will be helpful to students using Maple for the first time and professors who want their students to use Maple without needing to spend time learning the language.
 

In addition to the following post you can find a detailed video on using Maple to do Linear Algebra without programming here. You can also find some of the tools that are new to Maple 2020 for Linear Algebra here.

The biggest tools you'll be using are the Matrix palette on the left of Maple, and the Context Panel on the right of Maple.

First you should load the Student[LinearAlgebra] package by entering:

with(Student[LinearAlgebra]);

Once you have a Matrix you can use the context panel on the right to apply a variety of operations to it:

The Student Linear Algebra Menu will give you many linear algebra commands.

You can also access Maple's Tutors from the Tools Menu

Tools > Tutors > Linear Algebra

?Student[LinearAlegbra]

I have been using Alex Potapchik & & Alec Mihailovs' procedure for generating a multivariate sample

https://www.mapleprimes.com/questions/37539-Generate-Data-From-A-Multivariate-Normal

How can I plot the eigenvectors in the 3D scatterplot?

Download Plot_eigenvectors_in_3d_scatterplot.mw

How can I put a line to run from a single point on the x-axis to the top. Like a like that run at x = 5 axis to the top. 

Du plot two lines but overlapped 

how to set color of each line and choose each line plot on top of layer to confirm overlapped?

When I tried these ODE's in Maple 2019, and Maple 2018, they are worked (i.e. gave solutions). Now these ODE's either hang in 2020 or return unsolved. What could have caused this? On Maple 2020, under windows 10:

restart;
ode:=(x^2-1)*diff(y(x),x)^2-y(x)^2+1=0:
dsolve(ode); #hangs

restart;
ode:=(2*x^2+1)*diff(y(x),x)^2+(y(x)^2+2*x*y(x)+x^2+2)*diff(y(x),x)+2*y(x)^2+1=0:
dsolve(ode); # return unsolved

restart;
ode:=x*y(x)^2*diff(y(x),x)^3-y(x)^3*diff(y(x),x)^2+x*(x^2+1)*diff(y(x),x)-x^2*y(x):
dsolve(ode); # return unsolved

restart;
ode:=(diff(y(x),x) = (-y(x)^2+4*a*x)^3/(-y(x)^2+4*a*x-1)/y(x)):
dsolve(ode); #hangs

I noticed that in Maple 2019.2 this problem is also there. But not in Maple 2019.  So something changed from after Maple 2019.

Here is worksheet on Maple 2018 that shows these worked there. But no longer work on Maple 2020. There might be more like these but these the ones I found so far.

issue.mw

Is it possible to define variables with "unit" % or ‰ in Maple?

c:=20%

does not work, it apparently gives you 20 multiplied with the result of the last calculation.

Hi folks!

Is there any way to make this kind of derivative?

If necessary, I can provide the original file here.

Thanks in advance for any help!

If I understand how to use vectors in Maple, I need to give the number of elements.  Is this correct?  I am working with vectors that I do not know the number of elements.  I can use a large number that will be greater than the required number of elements, but this does not seem to be a good solution.  The number of elements is 2000 for about 10 different vectors.  What is the best method to set up the victors for this application?

Can anyone help me to frame the equations in Fractional Reduced Differential Transform Method 

system of nonlinear ordinary differential equations
ds/ dt = b−γ s(t)− (δ s(t)(i(t) + βa(t)) /N − ε s(t) m(t) 
de/ dt = δ (s(t)(i(t) + βa(t))/ N + ε s(t) m(t) − (1−ϑ) θ e(t) − ϑ α e(t) − γ e(t) 
di/ dt = (1−ϑ) θ e(t) − (ρ + γ) i(t)
da/ dt = ϑ α e(t) − (σ + γ) a(t)
dr /dt = ρ i(t) + σ a(t) − γ r(t)
dm /dt = τ i(t) + κ a(t) − ω m(t) 

Good day to all.

I have a function, z(x,y), that I am interested in exploring. The contour plot returns the z-contours on the x-y grid (see attached).

Can anyone suggest a way in which I can now assign z to the vertical axis (instead of y), x to the horizontal axis, and plot the contours for various y-values?

Thanks in advance.

Contour_Plot_MaplePrimes.mw

How can I  get the "phase portrait including vector fields" and several trajectories of the following dynamical system in the polar coordinates (Note that the system is also in polar coordinate)??

(-(2*I)*c1*eta+c1*sqrt(-e0^2-4*eta^2))/e0 = c2, ((2*I)*c2*eta+c2*sqrt(-e0^2-4*eta^2))/e0 = -c1

How can we remove c1 from the expression of c2 and similarly c2 from c1?

Hi

I try to visualize and animate the hollow volume between two functions, but I do not have an optimal rendering

Ideas? Thanks

,Q1.mw

The worksheet below displays dual cones inside the unit sphere, but the Gauss-Bonnet formula (area of upper cone's spherical cap plus length of dual cone's intersection with unit sphere) does not equal 2*Pi.

Please find my error.

Dual_cones.mw

In Maple 2020, I clicked on "Math Apps" and then clicked on "Algebra & Geometry", followed by "Boy's Surface".

It is a set of 3 parametric equations in terms of {u,v}. I would like to eliminate u and v and turn this into a single "error" function in terms of (x,y,z) such that anywhere this function is zero, the original set of equations are satisfied for some value of {u,v}. (Ideally, the values of u and v could be determined as well, but that would be a bonus.)

I tried this:

alpha = 1;
u in [-Pi/2, Pi/2];
v in [0, Pi];
eq1 := x(u, v) = (sqrt(2)*cos(v)^2*cos(2*u) + cos(u)*sin(2*v))/(2 - alpha*sqrt(2)*sin(3*u)*sin(2*v));
eq2 := y(u, v) = (sqrt(2)*cos(v)^2*sin(2*u) - sin(u)*sin(2*v))/(2 - alpha*sqrt(2)*sin(3*u)*sin(2*v));
eq3 := z(u, v) = 3*cos(v)^2/(2 - alpha*sqrt(2)*sin(3*u)*sin(2*v));
eliminate({eq1, eq2, eq3}, {u, v});

but got no response and no error message.

Additionally, I tried explaining that I want a function f such that f(x,y,z)=0, but again got no response and no error message:

eq4 := f(x, y, z) = 0;
solve({eq1, eq2, eq3, eq4}, f);

Any ideas what I'm doing wrong?

Thank you!

-- Glenn