Order Book Depth and Positive Semi-Definiteness - Quant Trader Interview Question
Difficulty: Easy
Category: Market Microstructure
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Topics: order-book, linear-algebra, positive-semi-definite
Problem Description
Consider a simplified order book for a stock. Let $A$ be a matrix where each row represents the quantity available at a specific price level above the best bid (the ask side) and each column represents the quantity available at a specific price level below the best offer (the bid side). All quantities are positive. For example:
$A = \begin{bmatrix} 10 & 5 \\ 8 & 2 \end{bmatrix}$
where:
- Row 1: Ask quantity at level 1 (10) and level 2 (5)
- Row 2: Ask quantity at level 3 (8) and level 4 (2)
- C
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