In the world of Linear algebra, matrices play a very important role in terms of dealing with different kinds of concepts. The matrix is considered to be a regular form and rectangular array of numbers, symbols or expressions which have been arranged in the format of rows and columns in the world of mathematics. People can very simply perform different kinds of operations on the matrix for example- matrix addition, matrix multiplication, matrix subtraction and so on.
The matrix multiplication is also known as the Matrix product or the multiplication of two matrices which will help in producing a single matrix. Hence, this is considered to be a type of binary operation to be undertaken by the people on the matrices. If there are two matrices under the name of matrix A and matrix B then the product of two matrices will be considered as AB.
Whenever the case of the matrix being multiplied by the integer it will be referred to as matrix multiplication and in this particular system, it will include rows and columns. If the people multiply a particular matrix by the scalar value then it will be known as the scalar multiplication concept and in this particular system, it is very much important for the people to be clear about everything so that they indulge in the right kind of solutions throughout the process. Apart from this registering the kids on platforms like Cuemath is a good idea because this will help in ensuring that everything will be professionally undertaken without any kind of problematic scenario in the whole process.
To perform multiplication of two matrices it is very much important for the people to ensure that number of columns in the first matrix is always equal to the number of rows in the second matrix so that the resulting matrix product will always have the rows of the first matrix and columns of the second matrix. In this way, the order of the resulting matrix will be the matrix multiplication order. Being clear about this order of operations is very important so that people can multiply the matrix very easily without any kind of hassle.
Following is the process of how to multiply the matrices:
There has been a significant amount of work in recent years in this particular industry and normally there are four types of algorithms that have to be implemented:
- Iterative algorithm
- Conquering and dividing algorithm
- Sub cubic algorithm
- Parallel as well as a distributed algorithm
There are several kinds of rules to be followed in the whole process of Matrix multiplication and some of the rules are mentioned as follows:
- The product of two matrices will always be defined as the columns of the first and the rows of the second one.
- If the AB term is defined then the BA term will not be defined.
- If both A and B matrices are the square matrices of the same order then both AB and BA will be defined.
- If AB and BA both are defined then it will not always mean that AB is equal to BA.
- Suppose the product of two matrices is the zero matrices then it will not always mean that one of the matrices is a zero Matrix.
Different kinds of properties of the multiplicative systems have to be understood by the kids so that they are never confused in the whole process and being clear about the commutative property of multiplication is important. The matrix multiplication will never be commutative. On the other hand, being clear about the associative property of multiplication is another very important thing because this particular property is very well proved. It is also very much important for the kids to have a clear-cut idea about other properties like distributive property, multiplication identity property, dimension property and various other properties in this particular area so that they never face any kind of hassle in the whole process of indulging into calculations.