Ad definition of L.c.325.x: You are trying to divide a 4x1 column vector by a 1x5 row vector and you really expected that to work? Thats brave! What did you expect to get?
Is the 4x5 matrix what you expected and what you need? If yes, congratulation - you found a nice way to achieve what otherwise would have required some programming.
A quick look in the theory of vectors and matrices will tell you that you cannot divide anything by a matrix. It will also tell you that you can only take the inverse of a sqare matrix, not of an 1x4 nor an 4x1 vector. So why did it work in your sheet for the (transposed) 4x1 vector? Explanation is "implicit vectorization". Whenever you evaluate an expression in Mathcad containing vectors (and in MC thats only column vectors) and you use an operation which is not defined for vectors (like exponentialization) but only for scalars, Mathcad applies implicit vectorization. That means one by one every element of the vector is inserted in the expression (not the whole vector) and the expression is evaluated. The various results are collected and returned in a vector. So when you transposed t.plate, making it a column vector and applied the operator ^-1 on it, it is not interpreted as the inverse of a matrix (t.plate transposed is not square) but as the scalar reciprocal value. This is not defined for vectors so Mathcad vectorizes and takes the reciprocal value of every element of the vector t.plate.transposed.
See the following examples:
a*a: is the vector scalar product. Thats how multiplication is defined for vectors
a^2: squaring is not defined for vectors! So Mathcad applies vectorization and squares each vector element singly - the result is again a vector
The last one is again a*a but this time explicit vectorization is applied and so Mathcad is forced to work on the elements one by one.
EDIT: Here is away to get the same matrix you got - again no programming but using range variables which may give you better control and understanding of the outcome. Note that to access the elements of t.plate we have to use both matrix indices as its not a (column) vector:
Werner Exinger wrote:
A quick look in the theory of vectors and matrices will tell you that you cannot divide anything by a matrix. It will also tell you that you can only take the inverse of a sqare matrix, not of an 1x4 nor an 4x1 vector. So why did it work in your sheet for the (transposed) 4x1 vector? Explanation is "implicit vectorization". Whenever you evaluate an expression in Mathcad containing vectors (and in MC thats only column vectors) and you use an operation which is not defined for vectors (like exponentialization) but only for scalars, Mathcad applies implicit vectorization. That means one by one every element of the vector is inserted in the expression (not the whole vector) and the expression is evaluated. The various results are collected and returned in a vector. So when you transposed t.plate, making it a column vector and applied the operator ^-1 on it, it is not interpreted as the inverse of a matrix (t.plate transposed is not square) but as the scalar reciprocal value. This is not defined for vectors so Mathcad vectorizes and takes the reciprocal value of every element of the vector t.plate.transposed.
See the following examples:
a*a: is the vector scalar product. Thats how multiplication is defined for vectors
a^2: squaring is not defined for vectors! So Mathcad applies vectorization and squares each vector element singly - the result is again a vector
The last one is again a*a but this time explicit vectorization is applied and so Mathcad is forced to work on the elements one by one.
Well done with the explanation Werner. I think Mathcad should document the theory of vectors and matrices a little better.
For example how would one know that a function is not defined for vectors?
Mike
Werner Exinger wrote:
No, its the other way round - the logarithm of a vector would NOT need explicit vectorization but would be automatically vectorized. Furthermore in Mathcad vectorization only works for (column) vectors, not for other matrices.
I actually meant for the 'absolute operator' as you correctly specified.
Werner Exinger wrote:
There are not much operators or functions which are defined to work on vectors (+,-,*, absolute value), so most of the time Mathcad would apply implicit vecorization. Nevertheless I would suggest to use explicit vectorization in any case to be on the safe side.
That is good advice. I have just checked a selected few operators on the calculator:
Of those I checked it was only the multiplication and absolute functions which do not implicitly vectorize. I cannot see the logic.
I agree with your 'customizeable per option' suggestion.
