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Easy · Market Microstructure · Quant Trader interview question · order-book, linear-algebra, positive-semi-definite
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