Generalized Eigenspaces — Topic Summaries
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Abstract Linear Algebra 38 | Invariant Subspaces
Invariant subspaces are the key structural tool behind Jordan normal form: a subspace U of a vector space V is called invariant under a linear map L...
Abstract Linear Algebra 39 | Direct Sum of Subspaces
Direct sums of subspaces are introduced as the key tool for splitting a vector space into two parts that don’t overlap except at the zero vector—and...
Abstract Linear Algebra 37 | Fitting Index
Fitting index is introduced as the first point in the Jordan-chain ladder where the dimensions stop growing—an invariant that pinpoints when...
Abstract Linear Algebra 40 | Block Diagonalization
A linear map that respects a direct-sum decomposition of the space can always be represented by a block diagonal matrix—no mixing between the two...