Question

Given that $A^\alpha$ and $B_\beta$ ($\alpha, \beta = 1, 2, 3, \ldots, n$) are contravariant and covariant vectors, respectively, and by convention, any repeated indices are summed over. Which of the following expressions is/are tensors?

• A. $A^\alpha B_\beta$
• B. $\frac{A^\alpha B_\beta}{A^\alpha B_\alpha}$
• C. $\frac{A^\alpha}{B_\beta}$
• D. $A^\alpha + B_\beta$

Answer 1

Answer: (A), (B)

$A^\alpha B_\beta$

Answer 2

The correct Answers are (A):$A^\alpha B_\beta$,(B):$\frac{A^\alpha B_\beta}{A^\alpha B_\alpha}$