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3. Numerical Linear Algebra 91
2. EIGEN BASIS
Group of vectors are described as the vector space. All the vectors in the
space are spanned by the particular set of orthonormal basis known as Eigen
basis as described below. (i.e) Any vector in the space is represented as the
linear combination of Eigen basis.
2.1 Example 1
The two dimensional vector are randomly generated and are plotted as given
below. The vectors mentioned in the diagram are the Eigen vectors. It is
computed as follows.
• Compute the co-variance matrix of the generated two
dimensional vectors
• Compute the Eigen values and the corresponding Eigen vectors.
• Direction of the Eigen vectors computed are parallel to the
vectors mentioned in the diagram. Note that they are orthonormal
to each other.
In the above described example, Eigen vectors are E 1= [-0.2459 -0.9693]
and E 2 =[-0.9693 0.2459].
Figure 3-2. Vector space along with Eigen vectors
