Hi there
I would recommend to check out @balaji.ambresh ‘s link for getting deeper into t-SNE!
Linear transformation means that you can transform your vector x in a new space with a linear operation M x. Here M is a matrix. And M x is a matrix multiplication which is a linear operation because x is transformed in a linear way. If you want to visualise what the matrix multiplication is doing, see also this video on linear algebra.
Also: a matrix multiplication is the only way possible for a linear transformation from a vector to a vector, see also: The Matrix of a Linear Transformation — Linear Algebra, Geometry, and Computation.
An example for such a kind of linear transformation or projection is a principal component analysis (PCA), see also this thread: Does embedding projector use dimensional reduction? - #4 by Christian_Simonis or this article.
Please let me know if this answers your question, @someone555777!
Best regards
Christian