ZHANG, Ruda June 27, 2022:  More on matrix manifolds; update image. [e308705]
ZHANG, Ruda September 18, 2021:  Add length space and metric geometry. [8e75409]
ZHANG, Ruda July 20, 2021:  More on homogeneous space, common Riemannian symmetric spaces. [07e3197]
ZHANG, Ruda March 03, 2021:  Use mathcal for big O notation, to distinguish from the orthogonal group. [69caae9]
ZHANG, Ruda February 19, 2021:  More on Grassmannian; Jacobi field, conjugate point. [ffad0c9]
ZHANG, Ruda February 19, 2021:  Digitize vector and matrix norms. [d693a77]
ZHANG, Ruda February 15, 2021:  Add matrix manifolds, principal angles between subspaces, Riemannian logarithm. [c0a0430]
ZHANG, Ruda June 17, 2020:  Formatting. More on manifolds: integral manifold, distribution, foliation; covariant derivative along curve in submanifold; higher-order retraction. [c08c622]
ZHANG, Ruda June 05, 2020:  More on manifolds: curvature concepts; bounds for sectional and Ricci curvature. [0b35b68]
ZHANG, Ruda June 04, 2020:  The trace operator. [86cb2bb]
ZHANG, Ruda June 02, 2020:  Reorganize Differential Geometry and Calculus on Manifolds. More on manifolds: connection, Lie bracket, Riemannian submanifolds; hypersurface; sectional curvature. [bfeb838]
ZHANG, Ruda May 28, 2020:  More on manifold: geodesic, higher-order retraction, matrix manifolds, horizontal lift, C^k regular level set theorem, zero section, curvature. [22084b8]
ZHANG, Ruda May 28, 2020:  More on manifold: curvature [d894980]
ZHANG, Ruda May 17, 2020:  More on manifold: curvature; total covariant derivative; covariant Hessian; Hessian (operator); geodesic and metric completeness of Riemannian manifolds. [b40aaa2]
ZHANG, Ruda April 30, 2020:  More on Riemannian manifolds: geodesic ball, uniformly normal neighborhood, minimizing and locally minimizing curves, injectivity radius, geodesically convex subset. [7c43693]
ZHANG, Ruda April 26, 2020:  More on smooth/Riemannian manifolds: connection, covariant derivative, vector fields along a curve, parallel transport; Levi-Civita connection. [dfc6848]
ZHANG, Ruda April 18, 2020:  More on geodesic, exponential map, normal and Fermi coordinates, frames, etc. [10265b3]
ZHANG, Ruda April 18, 2020:  Topological and strong equivalent of norms and metrics. [c6ba1e3]
ZHANG, Ruda March 11, 2020:  Edit bootstrap. [b9359a7]
ZHANG, Ruda January 21, 2020:  More on Hilbert space. [67ff8bb]
ZHANG, Ruda January 20, 2020:  More on Riemannian manifolds. [debb35a]
ZHANG, Ruda January 18, 2020:  Convert math-text words to text only when the math symbols are ASCII only. [e4c945c]
ZHANG, Ruda December 05, 2019:  More on manifolds, from John Marshall Lee's textbooks. [6ba9029]
ZHANG, Ruda April 21, 2019:  More on analysis [ebac375]
ZHANG, Ruda March 19, 2019:  More on topolog and geometry. [8fdd7fa]
ZHANG, Ruda March 19, 2019:  Reformat notes on functional analysis. [df25f75]
ZHANG, Ruda March 18, 2019:  Notes on topology and geometry. [bfe63ec]