If the matrix A is symmetric, there's no difference between Ab and ATb.newphysist said:Hi,
I am new to Math so I am trying to get some intuition.
Let's say I have a matrix A of n x n and a vector B of n x 1 what is the difference between A x B and A' x B?
Multiplying a vector with a square matrix and its transpose involves different mathematical operations. When multiplying a vector with a square matrix, the vector is transformed into a new vector with different dimensions. On the other hand, when multiplying a vector with the transpose of a square matrix, the vector remains the same size but is transformed into a row or column vector depending on the orientation of the transpose.
The dimensions of the matrix and vector determine whether the multiplication is possible. For example, when multiplying a 3x3 matrix with a 3x1 vector, the result will be a 3x1 vector. However, if the dimensions do not match, the multiplication cannot be performed.
In linear algebra, multiplying a vector with a square matrix and its transpose is used to transform a vector into a new vector with different dimensions. This operation is often used in applications such as data analysis, image processing, and machine learning.
The order of multiplication does not affect the result when multiplying a vector with a square matrix and its transpose. This is because both operations result in the same transformation of the vector, regardless of the order in which they are performed.
No, the transpose of a square matrix cannot be used instead of multiplying with the original matrix. The transpose operation results in a different transformation of the vector, and therefore cannot be used interchangeably with the original matrix.