The Difference Between Element-wise Multiplication, Matrix Multiplication, and Dot Product Operations in MATLAB
Element-wise multiplication in MATLAB is carried out using the .*
operator. It performs multiplication of corresponding elements in two arrays or matrices.
Matrix multiplication in MATLAB is denoted by the *
operator. It multiplies the rows of the first matrix with the columns of the second matrix to produce a new matrix.
The dot product operation in MATLAB is performed using the dot()
function. It computes the sum of the products of corresponding elements in two arrays or vectors.
Examples:
Element-wise Multiplication:
Scenario: Calculating element-wise product of two matrices.
A = [1 2; 3 4];
B = [5 6; 7 8];
C = A .* B;
In this scenario, each element of matrix A
is multiplied with the corresponding element in matrix B
.
Matrix Multiplication:
Scenario: Performing matrix multiplication of two matrices.
A = [1 2; 3 4];
B = [5 6; 7 8];
C = A * B;
Here, the rows of matrix A
are multiplied with the columns of matrix B
to obtain the resulting matrix C
.
Dot Product:
Scenario: Calculating the dot product of two vectors.
A = [1 2 3];
B = [4 5 6];
C = dot(A, B);
The dot product operation computes the sum of the products of the corresponding elements in vectors A
and B
.
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