It is easy to check whether two matrices A and B are equal or not. For example,

Question

It is easy to check whether two matrices A and B are equal or not. For example, length (find (A ~= B)) should be 0 if they are equal and some­thing positive if they are not equal. Using this write a pseudocode that determines whether (a) the rows (b) the columns of a matrix U are or­thonormal (with respect to the standard inner product) or not. The input is one matrix and out is 'yes' or 'no'. (Matlab command for identity matrix is 'eye') Repeat previous problem for the elliptic inner product (|)C with respect to matrix C. The inputs are two matrices (one of them is C) and the output is 'yes' or 'no'.

Explanation / Answer

2. Pseudo code:

a)

Input: Matrix U

b)

Input: Matrix U

3.

a)

Input: matrix C

1.Find matrix A, A=<.|.>C

2.Find B=ATC

3.Ca=(B~=eye)

4.If Ca==0, Output Yes

b)

Input: Matrix C

1.Find matrix A, A=<.|.>C

2.Find B=ACT

3.Ca=(B~=eye)

4.If Ca==0, Output Yes

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