Matrices operations theory
Matrices additions and subtractions theory
The sum of two Matrices (Aij), (Bij) of the same dimension, is another matrix (Rij) of the same dimension and with generic term sij=aij+bij.
Therefore, to be able to add two matrices, they must have the same dimension
Addition of Matrices: (Aij) + (Bij) = (Aij + Bij)
Subtraction of Matrices: (Aij) – (Bij) = (Aij – Bij)
Matrix multiplications and division theory
For two matrices A and B can be multiplied, A · B, it is necessary that the number of columns in the first matrix be the same as the number of rows in the second one.
In this case, the product A · B = C is another matrix whose elements are obtained by multiplying each row of the first matrix by each column of the second vector, as follows:
The resulting matrix C has many rows as A and many columns as B
The matrix division is defined as the product of the numerator multiplied by the inverse matrix of the denominator. That is to say:
A/B = A·B-1
To multiply a number by a matrix it is multiplied the number by each matrix digit.
To divide a matrix by a number all the terms of the matrix are divided by the number.
You can download the App BioProfe READER to practice this theory with self-corrected exercises.