17 Is there an “inverted” dot product? 9 Intuition of Picard Iteration 5 Show that the Area of image = Area of object $\cdot |\det(T)|$? Where $T$ is a linear transformation from $R^2 \rightarrow R^2$ 4 $\frac{\alpha}{\alpha + \beta}\|u\|^2 + \frac{\beta}{\alpha + \beta}\|v\|^2 > \langle u, v\rangle$ is true? 4 Prove that $f$ is linear

### Reputation (1,984)

 +10 Intuition of Picard Iteration +10 Taylor Polynomial $\ln(1-x)$ +20 Show that the Area of image = Area of object $\cdot |\det(T)|$? Where $T$ is a linear transformation from $R^2 \rightarrow R^2$ +10 Is there an “inverted” dot product?

### Questions (3)

 12 Are the addition and multiplication of real numbers, as we know them, unique? 2 Is there a name for the property of a function that maps the empty set to zero? 2 Does this kind of $C^1$-diffeomorphism a contraction?

### Tags (75)

 30 linear-algebra × 11 17 terminology 23 real-analysis × 21 17 vectors 19 calculus × 11 14 analysis × 5 17 abstract-algebra 12 integration × 6 17 products 12 ordinary-differential-equations × 3