Question :
I know @
is for decorators, but what is @=
for in Python? Is it just reservation for some future idea?
This is just one of my many questions while reading tokenizer.py
.
Answer #1:
From the documentation:
The
@
(at) operator is intended to be used for matrix multiplication. No builtin Python types implement this operator.
The @
operator was introduced in Python 3.5. @=
is matrix multiplication followed by assignment, as you would expect. They map to __matmul__
, __rmatmul__
or __imatmul__
similar to how +
and +=
map to __add__
, __radd__
or __iadd__
.
The operator and the rationale behind it are discussed in detail in PEP 465.
Answer #2:
@=
and @
are new operators introduced in Python 3.5 performing matrix multiplication. They are meant to clarify the confusion which existed so far with the operator *
which was used either for elementwise multiplication or matrix multiplication depending on the convention employed in that particular library/code. As a result, in the future, the operator *
is meant to be used for elementwise multiplication only.
As explained in PEP0465, two operators were introduced:
 A new binary operator
A @ B
, used similarly asA * B
 An inplace version
A @= B
, used similarly asA *= B
Matrix Multiplication vs Elementwise Multiplication
To quickly highlight the difference, for two matrices:
A = [[1, 2], B = [[11, 12],
[3, 4]] [13, 14]]

Elementwise multiplication will yield:
A * B = [[1 * 11, 2 * 12], [3 * 13, 4 * 14]]

Matrix multiplication will yield:
A @ B = [[1 * 11 + 2 * 13, 1 * 12 + 2 * 14], [3 * 11 + 4 * 13, 3 * 12 + 4 * 14]]
Usage in Numpy
So far, Numpy used the following convention:

the
*
operator (and arithmetic operators in general) were defined as elementwise operations on ndarrays and as matrixmultiplication on numpy.matrix type. 
method/function
dot
was used for matrix multiplication of ndarrays
Introduction of the @
operator makes the code involving matrix multiplications much easier to read. PEP0465 gives us an example:
# Current implementation of matrix multiplications using dot function
S = np.dot((np.dot(H, beta)  r).T,
np.dot(inv(np.dot(np.dot(H, V), H.T)), np.dot(H, beta)  r))
# Current implementation of matrix multiplications using dot method
S = (H.dot(beta)  r).T.dot(inv(H.dot(V).dot(H.T))).dot(H.dot(beta)  r)
# Using the @ operator instead
S = (H @ beta  r).T @ inv(H @ V @ H.T) @ (H @ beta  r)
Clearly, the last implementation is much easier to read and interpret as an equation.
Answer #3:
@ is the new operator for Matrix Multiplication added in Python3.5
Reference: https://docs.python.org/3/whatsnew/3.5.html#whatsnewpep465
Example
C = A @ B