矩阵剖析与PCA实例

Matrix Analysis and PCA Examples

真正将线性代数这门抽象学科彻底实像化与实用化则必须掌握向量空间和矩阵变换的本质。从几何和代数两个层面证明矩阵与向量和矩阵与矩阵左右乘法的实际意义,以矩阵运动和线性映射的角度阐释矩阵相似以及特征类的根源,最后引入PCA降维这一经典算法,综合了基、矩阵变换、特征类、极限等原理知识,以图表+逻辑推理方式再一次加深对线性代数原理本质的理解。

To truly image and apply linear algebra as an abstract subject,we must master the essence of vector space and matrix transformation.We proves the practical significance of matrix and vector,and matrix and multiplication matrix from the geometric and algebraic levels at the same time;expounds the source of matrix similarity and characteristics from matrix movement and linear mapping;and introduces the classical algorithm of PCA multidimensional reduction,composites base,matrix transformation,characteristic and extremity,and deepens the understanding of the principle and essence of linear algebra through chart+logical reasoning.