- #1
Gear300
- 1,213
- 9
What would be the proof for matrix multiplication?...or just an explanation as to why its done the way its done.
Matrix multiplication is a mathematical operation that involves multiplying two matrices together to produce a new matrix. It is often used to solve systems of linear equations and to transform data in fields such as engineering, physics, and computer science.
In order to multiply two matrices, the number of columns in the first matrix must match the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. The elements of the new matrix are calculated by multiplying the corresponding elements in each row of the first matrix by the corresponding elements in each column of the second matrix, and then adding the products together.
Matrix multiplication involves multiplying two matrices together, while scalar multiplication involves multiplying a single scalar value (a number) by each element in a matrix. In matrix multiplication, the order of the matrices matters, whereas in scalar multiplication, the order does not matter.
No, for two matrices to be multiplied together, the number of columns in the first matrix must match the number of rows in the second matrix. If this condition is not met, the matrices cannot be multiplied.
The result of multiplying a matrix by its inverse is the identity matrix, which is a square matrix with 1s along the main diagonal and 0s everywhere else. This is because the inverse of a matrix "undoes" the effects of the original matrix, resulting in the identity matrix.