Computer Lecture-4

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The Identity Matrix
Identity matrices are matrices of various sizes with ones on the main diagonal and zeros elsewhere.
The function
eye(m,n)
returns an m-by-n rectangular identity matrix and

eye(n)
returns an n-by-n square identity matrix.

The Kronecker Tensor Product
The Kronecker product, kron(X,Y), of two matrices is the larger matrix formed from all possible products of the elements of X with those of Y. If X is m-by-n and Y is p-by-q, then kron(X,Y) is mp-by-nq. The elements are arranged in the following order:

[X(1,1)*Y X(1,2)*Y . . . X(1,n)*Y
. . .
X(m,1)*Y X(m,2)*Y . . . X(m,n)*Y]

X =
1 2
3 4

I=eye(2)
I=
0
1
kron(X,I) is
1 0 2 0
0 1 0 2
3 0 4 0
0 3 0 4

kron(I,X) is
1 2 0 0
3 4 0 0
0 0 1 2
0 0 3 4

Solving System of Linear Equations
Suppose the following system of equations:
x_1 -? x?_2+2x_3 - ? x?_4=-8
2x_1-2x_2+3x_3-3x_4=-20
x_1+? x?_2+ x_3 =-2
x_1-x_2+4x_3+3x_4 =4
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