This textbook introduces sparse and redundant representations with a focus on applications in signal and image processing. The theoretical and numerical foundations are tackled before the applications are discussed. Mathematical modeling for signal sources is discussed along with how to use the proper model for tasks such as denoising, restoration, separation, interpolation and extrapolation, compression, sampling, analysis and synthesis, detection, recognition, and more. The presentation is elegant and engaging. Sparse and Red undant Representations is intended for graduate students in applied mathematics and electrical engineering, as well as applied mathematicians, engineers, and researchers who are active in the fields of signal and image processing.

Lie group Lie algebras and representations an elementary introduction By Brian C.Hall.pdf. 此书从开始即从矩阵切入，从代数而非几何角度引入矩阵李群的概念。并通过定义运算的方式建立exponential mapping，并就此引入李代数。这种方式比起传统的通过“左不变向量场(Left-invariant vector field)“的方式定义李代数更容易为人所接受，也更容易揭示李代数的意义。最后，也有专门的论述把这种新的定义方式和传统方式联系起来。