Is ABCDEF = AB(C(D))EF for matricies

  • Thread starter eax
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In summary, the parentheses in the equation AB(C(D))EF for matrices indicate the order of operations for matrix multiplication. The equation can be rearranged in various ways as long as the order is maintained. It is valid for matrices of any size as long as the dimensions are compatible. To check if ABCDEF is equal to AB(C(D))EF, you can perform matrix multiplication and compare the resulting matrices. Other variations of this equation for matrix multiplication include (ABC)(DEF), (A)(BCD)(EF), and (A)(B)(CD)(EF).
  • #1
eax
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is ABCDEF = AB(C(D))EF for matricies? Also is ABCD(EFGH) = ABCDEFGH?

Thanks in advance!
 
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  • #2
eax said:
is ABCDEF = AB(C(D))EF for matricies? Also is ABCD(EFGH) = ABCDEFGH?
"Yes" to both, although I am not sure what C(D) means in terms of matrix multiplication.
 
  • #3
Yes, multiplication of matrices is "associative".
 

1. What is the significance of the parentheses in the equation AB(C(D))EF for matrices?

The parentheses in this equation indicate the order of operations for matrix multiplication. This means that the matrix C is multiplied by D first, and then the resulting product is multiplied by A, before finally being multiplied by B and E.

2. Can the equation AB(C(D))EF be rearranged in any other way?

Yes, the equation can be rearranged in multiple ways as long as the order of operations is maintained. For example, it could be written as (AB)(C)(D)(EF) or (A)(B)(CD)(EF).

3. Is the equation AB(C(D))EF valid for all sizes of matrices?

Yes, the equation is valid for matrices of any size as long as the dimensions of the matrices are compatible for multiplication. In other words, the number of columns in one matrix must match the number of rows in the other matrix.

4. How do I know if ABCDEF is equal to AB(C(D))EF for matrices?

To determine if these two expressions are equal, you can perform the matrix multiplication and compare the resulting matrices. If the resulting matrices are identical, then the expressions are equal.

5. Are there any other variations of this equation for matrix multiplication?

Yes, there are multiple variations for matrix multiplication, depending on the number and order of matrices being multiplied. Some other common variations include (ABC)(DEF), (A)(BCD)(EF), and (A)(B)(CD)(EF).

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