Linear Algebra for Machine Learning Part 4 — Linear Transformation and Eigendecomposition(EVD)

Linear Transformation :

Linear Transformation: anticlockwise rotation of vectors about origin

Additional notes & references:

Also there are many other operations that can be achieved by linear transformation matrices. For example, “Scaling”(multiplication by a diagonal matrix), “Reflection” etc. Refer below pages if you want to know more.

• harvard.edu
• uu.nl
• wikipedia.org
• wolfram.com

Eigendecomposition (a.k.a. Eigenvalue Decomposition or EVD):

Additional notes & references:

The eigenvectors of a symmetric matrix are orthogonal to each other(proof). That means they form “basis” of the orientation of the dataset. We will see the use of this property in the next blog about PCA.

• mit.edu
• harvard.edu
• wolfram.com

Graphical Representation

• http://setosa.io/ev/eigenvectors-and-eigenvalues

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All parts in this series —

Part 1 — Building Blocks

Part 2 — Matrices

Part 3 — System of Linear Equations

Part 4 — Linear Transformation and Eigendecomposition(EVD)

Part 5 — Singular Value Decomposition (SVD) and Matrix Pseudoinverse

Part 6 — Dimensionality Reduction and PCA