Rewind to the start of the paragraph: "Let \mathbf{x} be a random vector with N dimensions."
You're assumed to already know what a "random vector with N dimensions" is. It's very resonable then to also assume you know what expectations and covariances of random vectors are, and some of their basic properties, such as linearity of expectations and quadratic forms of covariance matrices, since all of these are typically taught in the same course.
You're assumed to already know what a "random vector with N dimensions" is. It's very resonable then to also assume you know what expectations and covariances of random vectors are, and some of their basic properties, such as linearity of expectations and quadratic forms of covariance matrices, since all of these are typically taught in the same course.