Results for

Edit 15 Oct 2025: Removed incorrect code. Replaced symmatrix2sym and symfunmatrix2symfun with sym and symfun respectively (latter supported as of 2024b).
The Symbolic Math Toolbox does not have its own dot and and cross functions. That's o.k. (maybe) for garden variety vectors of sym objects where those operations get shipped off to the base Matlab functions
x = sym('x',[3,1]); y = sym('y',[3,1]);
which dot(x,y)
/MATLAB/toolbox/matlab/specfun/dot.m
dot(x,y)
ans = 
which cross(x,y)
/MATLAB/toolbox/matlab/specfun/cross.m
cross(x,y)
ans = 
But now we have symmatrix et. al., and things don't work as nicely
clearvars
x = symmatrix('x',[3,1]); y = symmatrix('y',[3,1]);
z = symmatrix('z',[1,1]);
sympref('AbbreviateOutput',false);
dot() expands the result, which isn't really desirable for exposition.
eqn = z == dot(x,y)
eqn = 
Also, dot() returns the the result in terms of the conjugate of x, which can't be simplifed away at the symmatrix level
assumeAlso(sym(x),'real')
class(eqn)
ans = 'symmatrix'
try
eqn = z == simplify(dot(x,y))
catch ME
ME.message
end
ans = 'Undefined function 'simplify' for input arguments of type 'symmatrix'.'
To get rid of the conjugate, we have to resort to sym
eqn = simplify(sym(eqn))
eqn = 
but again we are in expanded form, which defeats the purpose of symmatrix (et. al.)
But at least we can do this to get a nice equation
eqn = z == x.'*y
eqn = 
dot errors with symfunmatrix inputs
clearvars
syms t real
x = symfunmatrix('x(t)',t,[3,1]); y = symfunmatrix('y(t)',t,[3,1]);
try
dot(x,y)
catch ME
ME.message
end
ans = 'Invalid argument at position 2. Symbolic function is evaluated at the input arguments and does not accept colon indexing. Instead, use FORMULA on the function and perform colon indexing on the returned output.'
Cross works (accidentally IMO) with symmatrix, but expands the result, which isn't really desirable for exposition
clearvars
x = symmatrix('x',[3,1]); y = symmatrix('y',[3,1]);
z = symmatrix('z',[3,1]);
eqn = z == cross(x,y)
eqn = 
And it doesn't work at all if an input is a symfunmatrix
syms t
w = symfunmatrix('w(t)',t,[3,1]);
try
eqn = z == cross(x,w);
catch ME
ME.message
end
ans = 'A and B must be of length 3 in the dimension in which the cross product is taken.'
In the latter case we can expand with
eqn = z == cross(sym(x),symfun(w)) % x has to be converted
eqn(t) = 
But we can't do the same with dot (as shown above, dot doesn't like symfun inputs)
try
eqn = z == dot(sym(x),symfun(w))
catch ME
ME.message
end
ans = 'Invalid argument at position 2. Symbolic function is evaluated at the input arguments and does not accept colon indexing. Instead, use FORMULA on the function and perform colon indexing on the returned output.'
Looks like the only choice for dot with symfunmatrix is to write it by hand at the matrix level
x.'*w
ans(t) = 
or at the sym/symfun level
sym(x).'*symfun(w) % assuming x is real
ans(t) = 
Ideally, I'd like to see dot and cross implemented for symmatrix and symfunmatrix types where neither function would evaluate, i.e., expand, until both arguments are subs-ed with sym or symfun objects of appropriate dimension.
Also, it would be nice if symmatrix could be assumed to be real. Is there a reason why being able to do so wouldn't make sense?
try
assume(x,'real')
catch ME
ME.message
end
ans = 'Undefined function 'assume' for input arguments of type 'symmatrix'.'