Question

Find the Canonical decomposition of 2014.

Answer 1

Answer:

The canonical decomposition of higher-order tensors is a key tool in multilinear algebra. First we review the state of the art. Then we show that, under certain conditions, the problem can be rephrased as the simultaneous diagonalization, by equivalence or congruence, of a set of matrices. Necessary and sufficient conditions for the uniqueness of these simultaneous matrix decompositions are derived. In a next step, the problem can be translated into a simultaneous generalized Schur decomposition, with orthogonal unknowns (A.-J. van der Veen and A. Paulraj, IEEE Trans. Signal Process., 44 (1996), pp. 1136-1155).

Answer 2

Concept:

Every positive integer can be written in a unique way as a product of prime numbers where the prime factors are written in ascending order. This is called as the canonical decomposition of a number. For example: The canonical decomposition of 2048 will be 2¹¹.

Given:

We are given a number:

2014

Find:

We need to find its canonical decomposition.

Solution:

The factors of 2014 will be:

2014 = 2 × 19 × 53.

So, the canonical decomposition of 2014 will also be:

2014 = 2 × 19 × 53.

Therefore, we get the canonical decomposition of 2014 as 2 × 19 × 53.

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