Matrix arithmetic
there is no difference
Vector matrix has both size and direction. There are different types of matrix namely the scalar matrix, the symmetric matrix, the square matrix and the column matrix.
The answer is yes, and here's why: Remember that for the eigenvalues (k) and eigenvectors (v) of a matrix (M) the following holds: M.v = k*v, where "." denotes matrix multiplication. This operation is only defined if the number of columns in the first matrix is equal to the number of rows in the second, and the resulting matrix/vector will have as many rows as the first matrix, and as many columns as the second matrix. For example, if you have a 3 x 2 matrix and multiply with a 2 x 4 matrix, the result will be a 3 x 4 matrix. Applying this to the eigenvalue problem, where the second matrix is a vector, we see that if the matrix M is m x n and the vector is n x 1, the result will be an m x 1 vector. Clearly, this can never be a scalar multiple of the original vector.
There 3 to 4 symbols of multiplication depending on the condition.If you are using computer for calculation the only symbol of multiplication is *.If you are using calculator the symbol for multiplication is x.If you are solving equation in paper the symbol for multiplication b/w variables are mostly represent by a dot(.) or the place is left empty. A.B or AxB the answer will be same is scalar calculation but will be different on vector calculation. If use scalar calculation 'AB' will also represent multiplication b/w two variables. But it is only applicable on variables.If we use scalar number in equation like 3(4-3)*3=9; here '3(' is representing the multiplication b/w the number and the bracket. If there is any number before a bracket without any symbol then this will show that the number is multiplying by the bracket values.
Matrix arithmetic
scalar multiplication
They give us different results. The dot product produces a number, while the scalar multiplication produces a vector.
There is no real difference between the two operations. Division by a scalar (a number) is the same as multiplication by its reciprocal. Thus, division by 14 is the same as multiplication by (1/14).
I think so. Copy and paste method could be used to prove this. But this is only my opinion.
A matrix IS an array so it is impossible to multiply a matrix without array. The answer to the multiplication of two matrices need not be an array. If the first matrix is a 1xn (row) matrix and the second is an nx1 (column) matrix, then their multiple is a 1x1 matrix which can be considered a scalar.
there is no difference
No. A scalar matrix is a diagonal matrix whose main diagonal elements are the same. Only if the diagonal elements are all 1 is it an identity matrix.
A matrix and a scalar is a matrix. S + M1 = M2. A scalar is a real number whose square is positive. A matrix is an array of numbers, some of which are scalars and others are vectors, square of the number is negative. A matrix can be a quaternion, the sum of a scalars and three vectors.
Multiply each element of the matrix by the scalar.
It is a scalar multiplier.
A scalar is any single number, like 27, while a matrix contains at least 2 numbers such as [27, 3].