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No. The number of columns of the first matrix needs to be the same as the number of rows of the second.
So, matrices can only be multiplied is their dimensions are k*l and l*m. If the matrices are of the same dimension then the number of rows are the same so that k = l, and the number of columns are the same so that l = m. And therefore both matrices are l*l square matrices.
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Do similar matrices have the same eigenvalues?
Yes, similar matrices have the same eigenvalues.
What is the condition for the addition of matrices?
The matrices must have the same dimensions.
Do similar matrices have the same eigenvectors?
No, in general they do not. They have the same eigenvalues but not the same eigenvectors.
What is linear combination in matrices?
If X1, X2 , ... , Xn are matrices of the same dimensions and a1, a2, ... an are constants, then Y = a1*X1 + a2*X2 + ... + an,*Xn is a linear combination of the X matrices.
22 matrix with 33 matrix multiplication?
It is not possible. The number of columns in the first matrix must be the same as the number of rows in the second. That is, matrices, X (kxl) and Y (mxn) can only be multiplied [in that order] if l = m.
