I have a calculation which involves dividing an expression which is the dot product of two 2-D column vectors (arrays) by another expression of the same kind. This quotient expression directly displays a correct result; however, if I try to store the quotient expression into a new variable it does not work, and displays the error message "Matrix must be square". I'm running version .89 (Build 8). This type of calculation is extremely common in mechanics problems so this is a serious issue.

Hello,

I hope I understood you well. Here is an example:
[MATH=eng]A←mat(1,2,3,3,1)[/MATH][MATH=eng]B←mat(6,5,6,3,1)[/MATH][MATH=eng]C←mat(6,7,5,3,1)[/MATH][MATH=eng]D←mat(6,1,-2,3,1)[/MATH]
This gives you the result:
[MATH=eng]{A*B}/{C*D}=1.03[/MATH]
This will give an arror of "Matrix must be square" if you do not supress Symbolic optimization:
[MATH=eng]C←{A*B}/{C*D}[/MATH]
If you right click on it and choose Optimization|Numeric or None you will have the numerical result:
[MATH=eng]C=1.03[/MATH]

Symbolic engine of SMath is going to interpred the dividing of two arrays A/B as A*inverse( B ). Therefore the array B must be a square matrix. You can avoid this by suppressing the Symbolic optimization. I hope I am right about it.

Regards,
Radovan

Subtle SMath difference in the multiplication of two vectors.

For two column vectors A and B, A*B is the dot product, and equal 34 in the example above.

More rigorously AT*B ( A transpose times B ) is the dot product.

If A were a row vector A*B would return a matrix (34) using the values for A and B above.

Doesn't solve the problem but interesting.

Thank you Ed for the comment

Wrote

For two column vectors A and B, A*B is the dot product, and equal 34 in the example above.

More rigorously AT*B ( A transpose times B ) is the dot product.

If A were a row vector A*B would return a matrix (34) using the values for A and B above.

It seems you are right:
[MATH=eng]A*B=34[/MATH]
[MATH=eng]transpose(A)*B=mat(34,1,1)[/MATH]
I am in doubt now, as well as you are, that these two expressions should be the same and both should give a scalar. I am not quite sure about it. One explanation could be that the dot product is defined as the product of two vectors (column matrix). The second one might be ragarded as a matrix operation giving a matrix. However, I am also puzzled here:
[MATH=eng]{transpose(A)*B}/{transpose(C)*D}=1.03[/MATH]
I think this should be considered as a matrix expression and to give a matrix - but, surprisingly, it gives a scalar ???

Regards,
Radovan

Fala mnogu Radovan. Your first post solved my problem. Clark N.

Wrote

Fala mnogu Radovan. Your first post solved my problem. Clark N.

You are welcome Clark
Just do not hesitate to ask whatever you need. Someone will help you here.

Regards,
Radovan

Wrote

if I try to store the quotient expression into a new variable it does not work, and displays the error message "Matrix must be square".

_________________ Few more ... "Matrix must be square" __________________

You can try using "Local variable definition"

I have 3 examples of compulsory "Local var def"
1. De Boor spline
2. Quadratic spline coeficients
3. Cubic l_p_c_splinecoefficients

Work sheet would help.

Jean