aXb

$$\underset{1\times m}{a}\cdot\underset{m\times n}{X}\cdot\underset{n \times1}{c}=\sum a_{i}X_{ij}c_{j}$$

• This can also be extended to blocks of matrices.

implemetation 1:

If matrix A is a positive definite matrix, then -A is not (However it is full rank).

• The diagonal elements of a positive definite matrix will be positive.

• Suppose a=[0,...,0,1,0,...,0], then $a \cdot(-A)\cdot a$ can be diagonal element in -A. For -A, it is negative. Thus, -A is not positive definite.