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Suppose n is a positive integer. Define

T∈L(Fⁿ) by
T(z₁​,…,zₙ​)=(0,z₁​,…,zn₋₁​).
Find a formula for T*(z₋₁​,…,zₙ​).

User Aupajo
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1 Answer

6 votes

Final answer:

The formula for T*(z₋₁​,...,zₙ​) is T*(z₋₁​,...,zₙ​) = (0,z₋₁​,...,zₙ​).

Step-by-step explanation:

To find the formula for T*(z₋₁​,…,zₙ​), we first need to understand what T*(z₋₁​,…,zₙ​) represents.

The symbol T* denotes the adjoint of the linear operator T.

In other words, T* is the transpose of T.

In this case, T(z₁​,…,zₙ​)=(0,z₁​,…,zn₋₁​), so T* will be a linear operator that takes a vector (z₋₁​,…,zₙ​) and returns a vector of the same dimensions, where the first element is 0 and the remaining elements are the same as in the input vector.

Therefore, the formula for T*(z₋₁​,...,zₙ​) is T*(z₋₁​,...,zₙ​) = (0,z₋₁​,...,zₙ​).

User Yone
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