Category: Science or Scientasy

[If the equations are not visible please try refreshing the page] A linear transformation f is a transformation maintaining the following two properties: Any linear transformation can be represented using a matrix multiplication with a vector. Any linear transformation splits the n-dimensional space V into k f-invariant subspaces – direct sum of which returns the original space, V. These subspaces show eigenvector-like property i.e. when any vector from such a subspace is transformed using then where is a scaler value. Now, when all these f-invariant subspaces are one-dimensional, then the basis vector of each such one-dimensional vector is called an …