How do I apply operations to a symbolic array?

Hi all,

I am preparing a program for symbolic Geometric Algebra computation and I am facing a problem that requires your help. My vectors will be represented in matrix form and there are many operations that need to be performed.

For example when matrix A is a double array:

A=[1 2 0; 4 0 6];
A>0

returns a logical matrix

[1   1   0;1   0   1]

However, when I set the following symbolic matrix:

syms C
a=sym(A);
a(1)=C;

a=[ C, 2, 0]

[ 4, 0, 6]

How do I apply an operation to this symbolic matrix to return the following logical matrix?

[1 1 0;1 0 1]

Thank you for your help.

[Karan Gill]

Adding to the answer, use assumptions, then isAlways: https://www.mathworks.com/help/symbolic/assumptions-for-symbolic-objects.html

[ash ash]

Thank you!

Answer 1

[Star Strider]

Use the isAlways function:

syms C 
A = sym([1 2 0; 4 0 6]);
L = isAlways(A > 0)

L =

    2×3 logical array

     1   1   0
     1   0   1

However:

syms C 
A = sym([1 2 0; 4 0 6]);
A(1,1) = C;
L = isAlways(A > 0)

produces:

Warning: Unable to prove '0 < C'. 
> In symengine
  In sym/isAlways (line 38)
  In Elipses (line 79024) 

L =

    2×3 logical array

     0   1   0
     1   0   1

while setting a condition on ‘C’ produces:

syms C 
assume(C, 'positive')
A = sym([1 2 0; 4 0 6]);
A(1,1) = C;
L = isAlways(A > 0)

L =

    2×3 logical array

     1   1   0
     1   0   1

[ash ash]

Thank you very much!

[Star Strider]

As always, my pleasure!