Dot product
- Applies to one dimensional arrays, aka vectors.
- The sum of the products of the components of the vectors.
- The result supposedly represents “how similar the two vectors are”.
- The first elements of each vector multiplied, then the second, third, etc. Then add them all together.
- Aka inner product
- Aka scalar product. Since the result is a scalar.
- Notation is the two vector names next to each other with a superscripted T above the first.
- In Numpy, the dot method of the first vector is called, passing the second vector as an argument.
Hadamard product
- Can do this on vectors of the same size.
- Result is a vector also that same size.
- The first elements of each vector multiplied and become the first element of the answer. Repeat for all elements.
- Notation is a very small centered circle between the elements.
- In Numpy, the * operator is used.
Matrix multiplication
- Applies to arrays with dimensions higher than one.
- Technically when there is only one dimension in either or both arrays, it is the same process described here, but each row and/or column have only one element, so it can be simpler to think of it only in terms of the "Dot Product" description above.
- In Numpy, a matrix will be an array of arrays
- Can multiply two matrices A and B if the number of [rows, columns] in matrix A is equal to the number of [columns, rows].
- Result is another matrix with the width of B and the height of A.
- Each element of the result is a scalar.
- Each element of the result is the dot product of corresponding rows of A with columns of B.
- The first row of the result is the dot product of the first row of A with each of the columns of B.
- The second row of the result is the dot product of the second row of A with each of the columns of B.
- And so on.
- Notation is the names of the two matrices next to each other.
- In Numpy, the dot method of the first array is called, passing the second array as an argument.
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