Hello

Consider the following three kind of matrices. are there any
properties such as inverse or Eigenvalues or determinant or etc
specific to these kind of matrices:

1-In each row the sum of square of each element is 1.

2-In each row the sum of square of each element is 1 And In each
column the sum of square of each element is 1

3-if t1,t2,..,tn are either real or complex numbers we construct the
matrix as follows :
|t1| t1 t1 t1 t1
t1' |t2| t2 t2 t2
t1' t2' |t3| t3 t3
t1' t2' t3' |t4| t4
t1' t2' t3' t4' |t5|

What is ' ?  Complex conjugate?

By "sum of square" do you mean "sum of squares of absolute values" in the
complex case?

david.a... at (no spam) gmail.com writes:
Hello

Consider the following three kind of matrices. are there any
properties such as inverse or Eigenvalues or determinant or etc
specific to these kind of matrices:

1-In each row the sum of square of each element is 1.

2-In each row the sum of square of each element is 1 And In each
column the sum of square of each element is 1

3-if t1,t2,..,tn are either real or complex numbers we construct the
matrix as follows :
|t1|       t1      t1      t1      t1
t1'        |t2|    t2      t2      t2
t1'        t2'     |t3|    t3      t3
t1'        t2'     t3'     |t4|    t4
t1'        t2'     t3'     t4'     |t5|

What is ' ?  Complex conjugate?

By "sum of square" do you mean "sum of squares of absolute values" in the
complex case?
--
Robert Israel              isr... at (no spam) math.MyUniversitysInitials..ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

Hello

Consider the following three kind of matrices. are there any
properties such as inverse or Eigenvalues or determinant or etc
specific to these kind of matrices:

1-In each row the sum of square of each element is 1.

2-In each row the sum of square of each element is 1 And In each
column the sum of square of each element is 1

3-if t1,t2,..,tn are either real or complex numbers we construct the
matrix as follows :
|t1|    t1      t1      t1      t1
t1'     |t2|    t2      t2      t2
t1'     t2'     |t3|    t3      t3
t1'     t2'     t3'     |t4|    t4
t1'     t2'     t3'     t4'     |t5|

Thank you for your help
Best regards,

I think the eigenvalues are real and less than or equal to 1 since
A`*A is a real symmetric matrix and all values are less than 1. You
should test it out with some examples to make sure I'm correct. I
could be wrong, I'm just working off a vague memory from over 20 years
ago.

Hello,