Hi, in Matlab I encounter with two new operations for me which are array multiplication and array division. I want to learn that do they have physical applications in real world physics problems or are they be related with banking and accounting.
Array multiplication is a fairly common operation. I'm not sure what 'array division' is. Array multiplication can mean, for example, the dot product between two n x 1 arrays or multiplying two rectangular arrays together to obtain another rectangular array (m x n) x (n x p) = (m x p), where m, n, and p represent the dimensions of the various arrays in the format (no. or rows x no. of columns). Arrays are used widely in math and science (you may have encountered the term 'matrix'; 'matrix' is another name for an array). Can you provide a clearer picture of 'array division'?
Sorry it was a right or left division on an array. But in Matlab we can divide an array such as matrix by another array. I think the example you give on array multiplication is not what I mean. It is different than scalar and cross products in mechanics we learn. I see array multiplication while studying Matlab and it produces an array again but scalar product not. It is also different than matrix multiplication as well.
Look like it's just a method within matlab that allows someone to modify the elements of the array quickly. It's important to not confuse the data structure of an array with the concept of vector or in the case of a double array, matrix.
Confusing array with a vector and a matrix? But both vectors and matrices are already arrays. I think array multiplication is a new type of multiplication, multiplication of element to element. It can both applied to matrices and vectors so it is not important to confuse any data structure. Is it correct?
Not quite. In programming, we often represent vectors and matrices as arrays. In programming arrays are data structures (and data types). It's useful to take the array data structure and input numbers into the memory locations for and create objects that resemble what we know as vectors and matrices. Once you do that you can begin to perform operations on the object that reflect matrix operations. However, as you've just seen, you can also modify the array in a way a normal vector and matrix cannot be modified. What is happening here is a method that exist within matlab that modifies the elements in the data sucture, quickly.
There are applications where an element-by-element product of two arrays (##C_{ij} = A_{ij}B_{ij}##) is useful. Matlab provides this operation because it does have utility. This is not matrix multiplication. It's something different.