Linear Algebra · Advanced · 11 min
Null space
The null space consists of exactly the inputs a transformation sends to zero.
WHAT HAPPENS IF…Does a zero-dimensional kernel mean the kernel is empty?
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For A(0), all multiples of (−2,1) vanish. If t≠0, that direction maps to (0,tq), and only the zero vector is in the kernel. For the zero matrix every input is in the kernel. The resulting nullities 1,0,2 complement ranks 1,2,0.
A detail that matters
A tiny nonzero output is not exactly a null vector.
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