Beginning Anomaly Detection Using

Square Matrix vs. Transposed Square Matrix (Figure 

5-6

)

1

5

4

2

A =

1  5  4  2

A

T

=

Figure 5-5.  Original vector vs. its transposed version

B =

B

T

=

1  2  3

4  5  6

7  8  9

1  4  7

2  5  8

3  6  9

Figure 5-6.  Original matrix vs. its transposed self. Note how the entries seem to be 

flipped along the diagonal

Vector vs. Transposed Vector (Figure 

5-5

)

Matrix (nxm) vs. Transposed Matrix (mxn) (Figure 

5-7

)

C =

C

T

=

1  2 

3  4 

5  6 

1  3  5

2  4  6

Figure 5-7.  Original nxm matrix vs. its transposed mxn self. The columns of the 

original matrix C become the rows of the transposed matrix C

T

Rewriting the summations to reflect the multiplication of the respective vectors, one 

being transposed, the energy function is equivalent to the equation in Figure 

5-8

.

Figure 5-8.  The equivalent formula for the energy function written without 

summations

Using the energy function, we can define a