Rank-Nullity Theorem — Topic Summaries
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Linear Algebra 35 | Rank-Nullity Theorem
Rank–nullity theorem is the organizing rule behind how linear maps “trade” dimensions: for any linear map represented by a matrix with n columns, the...
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 29 | Rank gives Equivalence
Equivalent matrices—those related by changes of bases in the domain and codomain—can represent the same linear map even though their entries differ....