I have to define a state space equation. there is a vector with 5 members as stats such that all states(members of the vector) are real numbers.

which notation is true for this case?

x=[x1,x2,x3,x4,x5] ∈ R


x=[x1,x2,x3,x4,x5] ∈ R^5

where ^ implies that the number 5 is the power of R

is both are correct. which one can I use to introduce my states?


closed as off-topic by max_zorn, Morgan Rodgers, Javi, mrtaurho, Lee David Chung Lin Apr 24 at 0:17

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    $\begingroup$ The second one is the correct one. $\endgroup$ – Botond Apr 23 at 16:50

In general, the symbol $\mathbb R^n$ is used to denoted the vector space of $n$-dimensional real vectors. The symbol $\mathbb R$ is typically used to denote the set/field of real numbers, not a vector space.

With this in mind, both of the following notations would likely be readily understood:

$$\mathbf x =\langle x_1, x_2, x_3, x_4, x_5 \rangle, \quad \mathbf x \in \mathbb R^5$$ or $$\mathbf x =\langle x_1, x_2, x_3, x_4, x_5 \rangle, \quad x_i \in \mathbb R$$

  • $\begingroup$ Actually $\Bbb R$ is a vector space... $\endgroup$ – David C. Ullrich Apr 23 at 19:04

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