How to Check if Matrix Multiplication is Validīefore writing Python code for matrix multiplication, let’s revisit the basics of matrix multiplication. Matrix Multiplication between two matrices A and B is valid only if the number of columns in matrix A is equal to the number of rows in matrix B. However, have you ever wondered why this is the case? You’d have likely come across this condition for matrix multiplication before. Well, it’s because of the way matrix multiplication works. In our generic example, matrix A has m rows and n columns. The element at index (i, j) in the resultant matrix C is the dot product of the row i of the matrix A, and column j of the matrix B. So to get an element at a particular index in the resultant matrix C, you’ll have to compute the dot product of the corresponding row and column in matrices A and B, respectively. In the above generic example, every row in matrix A has n elements.So for the dot product between a row and a column to be valid-when multiplying two matrices-you’d need them both to have the same number of elements.It’s evident that the dot product is defined only between vectors of equal length.Repeating the process above, you’ll get the product matrix C of shape m x p-with m rows and p columns, as shown below.Īnd the dot product or the inner product between two vectors a and b is given by the following equation. And every column in matrix B has n elements too. If you take a closer look, n is the number of columns in matrix A, and it’s also the number of rows in matrix B. And this is precisely the reason why you need the number of columns in matrix A to be equal to the number of rows in matrix B. I hope you understand the condition for matrix multiplication to be valid and how to obtain each element in the product matrix. Let’s proceed to write some Python code to multiply two matrices. Write a Custom Python Function to Multiply MatricesĪs a first step, let us write a custom function to multiply matrices. Accept two matrices, A and B, as inputs.Check if matrix multiplication between A and B is valid.

If valid, multiply the two matrices A and B, and return the product matrix C.Else, return an error message that the matrices A and B cannot be multiplied.Step 1: Generate two matrices of integers using NumPy’s random.randint() function. You can also declare matrices as nested Python lists. Step 2: Go ahead and define the function multiply_matrix(A,B). Return 'Sorry, cannot multiply A and B.' Parsing the Function Definition def multiply_matrix(A,B):Ĭ = np.zeros((A.shape,B.shape),dtype = int) This function takes in two matrices A and B as inputs and returns the product matrix C if matrix multiplication is valid. Let’s proceed to parse the function definition.ĭeclare C as a global variable: By default, all variables inside a Python function have local scope. And you cannot access them from outside the function.

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