Linear Algebra Operations

TensorFlow offers a suite of functions dedicated to linear algebra operations, making matrix operations straightforward.

Matrix Multiplication

Here's a quick reminder of how matrix multiplication works.

There are two equivalent approaches for matrix multiplication:

• The tf.matmul() function;
• Using the @ operator.

Note

Multiplying matrices of size 3x2 and 2x4 will give a matrix of 3x4.

Matrix Inversion

You can obtain the inverse of a matrix using the tf.linalg.inv() function. Additionally, let's verify a fundamental property of the inverse matrix.

Note

Multiplying a matrix with its inverse should yield an identity matrix, which has ones on its main diagonal and zeros everywhere else. Additionally, the tf.linalg module offers a wide range of linear algebra functions. For further details or more advanced operations, you might want to refer to its official documentation.

Transpose

You can obtain a transposed matrix using the tf.transpose() function.

Dot Product

You can obtain a dot product using the tf.tensordot() function. By setting up an axes argument you can choose along which axes to calculate a dot product. E.g. for two vectors by setting up axes=1 you will get the classic dot product between vectors. But when setting axes=0 you will get broadcasted matrix along 0 axes:

Note

If you take two matrices with appropriate dimensions (NxM @ MxK, where NxM represents the dimensions of the first matrix and MxK the second), and compute the dot product along axes=1, it essentially performs matrix multiplication.