Is Scalar Multiplication of Vectors Written Without Parentheses?

[C0nfused]

Hi everybody,
I have a small question. I know that we have defined multiplication of a number and a vector ,for example b*A (capital letters =vectors, everything else=real numbers). We have also defined that b*(c*A)=(b*c)*A. From these two rules is a*b*c*d*...*k*Z defined (= product of n numbers with a vector) without using parentheses? What about a*b*c*E*D ? And one last thing: is scalar multiplication also written with juxtaposition? For example the above examples can be written like this: abcd...kZ and abcE*D ?
Thanks

 

[cronxeh]

You can multiply a scalar by a matrix anytime you want. However in order to multiply a matrix by another matrix their size has to be compatible.

A_{m x n} * B_{n x p}. For example,
A _ {2 x 3} = \left(<br /> \begin{array}{x1x2x3}<br /> 2 &amp; 4 &amp; 3\\<br /> 1 &amp; -1 &amp; 5\\<br /> \end{array}<br /> \right)<br /> can only be multiplied by a matrix which is in B_{3 x n} form.

So let B_{3x5}= \left(<br /> \begin{array}{x1x2x3x4x5}<br /> 1 &amp; 0 &amp; 5 &amp; 2 &amp; 3\\<br /> 0 &amp; -1 &amp; 2 &amp; 4 &amp; 1\\<br /> 4 &amp; 5 &amp; 6 &amp; 7 &amp; 8<br /> \end{array}<br /> \right)<br />

The resulting matrix will be A_{2x3} * B_{3x5} = C_{2x5}
C_{2x5} = \left(<br /> \begin{array}{x1x2x3x4x5}<br /> 14 &amp; 11 &amp; 36 &amp; 41 &amp; 34\\<br /> 21 &amp; 26 &amp; 33 &amp; 33 &amp; 42\\<br /> \end{array}<br /> \right)

If you have (a*b*c*d) * (A_{3x5} * B_{5x4} * C_{4x7} The resulting matrix will be: (a*b*c*d) * (M_{3x7})

 

[jcsd]

Hi everybody,
I have a small question. I know that we have defined multiplication of a number and a vector ,for example b*A (capital letters =vectors, everything else=real numbers). We have also defined that b*(c*A)=(b*c)*A. From these two rules is a*b*c*d*...*k*Z defined (= product of n numbers with a vector) without using parentheses? What about a*b*c*E*D ? And one last thing: is scalar multiplication also written with juxtaposition? For example the above examples can be written like this: abcd...kZ and abcE*D ?
Thanks

a*b*c*E*D is not defined without first defining the multiplication of two vectors (so in otherwords you'd have to say exactly what E*D means).

It is usual to use juxtapostion for the multiplication of two scalars or the multiplication of a scalar by a vector. As there is more than one kind of product of two vectors, it's usual to use whatever binary operator denotes that product to avoid confusion.

 

[C0nfused]

Thanks for your answers