# What is linear transformation?

Linear function?

Have you seen this ?

Yes, I saw in lecture and understand, that analogies are recognized by clusters. But I can’t understand what means “linear transformation”.

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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.