Linearity — Topic Summaries
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Real Analysis 50 | Properties of the Riemann Integral for Step Functions [dark version]
For step functions, the Riemann integral behaves exactly like a well-behaved “oriented area” functional: it turns a step function into a real number...
Linear Algebra 19 | Matrices induce linear maps [dark version]
A matrix doesn’t just store numbers—it automatically defines a linear map between vector spaces, and the usual matrix-vector multiplication is...
Linear Algebra 31 | Inverses of Linear Maps are Linear [dark version]
Inverses of bijective linear maps are themselves linear—so once a linear map is invertible, there’s no need to re-check linearity for its inverse....