Please, write to the Lecturer for more precise explanations on exercises to
solve in order to be evaluated for his course.

Some exercises are described below, but these descriptions can be
incomplete and contain mistakes.

prof Tyrtyshnikov asked to the students to show that for every versor there
exists a tensor train which can be obtained in a finite number of operations
(first lecture) and a tensor train with r_k=rank(a_k) for every k (third
lecture); in the third lecture he also asked us to represent the sum
of two given versors as tensor train; in his last lecture in Moscow he asked to
show that A Kroneckerproduct B has columns rank maximum (when A and B
have linearly independent columns), and that spark-1=kruskal rank , and that
k_A k_B k_C >= 2R+2 implies that A Kroneckerproduct B has columns rank
maximum.

prof Matveev in his first lecture asked to the students to prove that
A=CB^{-1}R where A is a matrix with not maximum rank, R and C are
respectively adiacent rows and columns of A, and B is their
"intersection"; in his second lecture he asked to implement the algorithm
for cross sampling with the following functions:
i^aj^b+i^bj^a  and (i+j)^{1/2} with a=1/2, b=1/3 and the values of n
2^10 2^12 2^14 , and stopping criterium ||UpOp|| < Epsilon^2, and to
calculate te cost with tensor train of  \sum_{i1} from 1 to n
\sum_{i1} from 1 to n  A_{i1,i2^n i1^n i2}