JOHN

### Questions (54)

 5 What inspires people to define linear maps? 4 Why linear maps act like matrix multiplication? 4 Why we only need to verify additive identity, and closed under addition and scalar multiplication for subspace? 3 Suppose $T: V \to W$, why matrices are used as a method of recording the values of the $Tv_j$'s in terms of a basis of $W$? 3 What topics I need to cover in order to understand Black Scholes Option Pricing Model?

### Reputation (458)

 +20 Why linear maps act like matrix multiplication? +5 Proof of Matrix Multiplication +5 Prove that $V = \text{null }\varphi \oplus \{au:a \in \mathbb{F}\}$ +5 Can I say dim range $T =$ dim null $S$ + range $S$ if $S \in \mathcal{L}(V,W)$, and $T \in \mathcal{L}(U,V)$?

 5 What's wrong with this proof by contradiction (Session 3.3 of How to prove it)? 1 Prove the set of continuous real-valued functions on the interval [0,1] is a subspace of R[0,1] 0 Proof of $j=1$ where $v_j \in span(v_1, …,v_{j-1})$

### Tags (16)

 5 logic × 6 0 linear-transformations × 19 5 proof-verification × 4 0 matrices × 2 1 linear-algebra × 48 0 proof-writing 1 proof-explanation × 6 0 summation 1 epsilon-delta × 2 0 statistics

### Accounts (10)

 Mathematics 458 rep 9 Stack Overflow 278 rep 415 Geographic Information Systems 177 rep 18 Mathematics Educators 141 rep 4 Philosophy 123 rep 3