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1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

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1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

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Earth and Space Sciences · 术语表

什么是 Orientation tensor？

Definition 8.5 University Earth and Space Sciences — Year 3 · 第 8 章 — Structural Analysis

The orientation tensor of $N$ unit vectors $\vec p_1, \dots, \vec p_N$ is the symmetric matrix

T = \frac1N\sum_{i=1}^N \vec p_i\,\vec p_i^{\mathsf T}, \qquad T_{jk} = \frac1N\sum_i p_{ij}\,p_{ik} .

It does not change when a vector is replaced by its opposite, so it suits axes and poles, which have no sense. Its eigenvalues $\lambda_1 \ge \lambda_2 \ge \lambda_3 \ge 0$ add up to its trace, $1$ .

Pi-diagram of the Varden anticline on the equal-area net, lower hemisphere: the poles of twelve bedding readings (dots), the best-fit girdle from the orientation tensor (blue), the great circles of the two mean limbs (dashed) and the beta-axis (triangle), where all three great circles meet. A bed dipping east has its pole to the west of the centre.

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