# How does a 3D, 4D,.. hyperplane look like (visualization)?

I am looking at support vector machine classification algorithm.

It finds the optimal hyperplane. In linear algebra, hyperplane is a space that is one dimension lower than the ambient plane. For example, in a 2D space, the hyperplane is a 1D line. In a 3D space, the hyperplane is a 2D plane. The following image shows such examples.

I am interested to see the visualization of the hyperplane beyond 2D. For example: 3D, 4D...

As you can see from your examples a hyperplane of dimension $$n$$ is visualized in $$n+1$$ dimensional space. This goes basically back to the definition of hyperplane: