斯坦福大学机器学习课程讲义第三讲-线性代数基础.pptx

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1、Linear Algebra review(optional),Matrices and vectors,Machine Learning,Dimension of matrix:number of rows x number of columns,Matrix:Rectangular array of numbers:,Matrix Elements(entries of matrix),“,entry”in the row,column.,Vector:An n x 1 matrix.,n-dimensional vector,1-indexed vs 0-indexed:,element

2、,Linear Algebra review(optional),Addition and scalar multiplication,Machine Learning,Matrix Addition,Scalar Multiplication,Combination of Operands,Linear Algebra review(optional),Matrix-vector multiplication,Machine Learning,Example,Details:,m x n matrix(m rows,n columns),n x 1 matrix(n-dimensionalv

3、ector),m-dimensional vector,To get,multiply s row with elements of vector,and add them up.,Example,House sizes:,Linear Algebra review(optional),Matrix-matrix multiplication,Machine Learning,Example,Details:,m x n matrix(m rows,n columns),n x o matrix(n rows,o columns),m x omatrix,The column of the m

4、atrix is obtained by multiplying with the column of.(for=1,2,o),Example,House sizes:,Matrix,Matrix,Have 3 competing hypotheses:,1.,2.,3.,Linear Algebra review(optional),Matrix multiplication properties,Machine Learning,E.g.,Let,Let,Compute,Compute,Identity Matrix,For any matrix,Denoted(or).Examples

5、of identity matrices:,Linear Algebra review(optional),Inverse and transpose,Machine Learning,Not all numbers have an inverse.,Matrix inverse:If A is an m x m matrix,and if it has an inverse,Matrices that dont have an inverse are“singular”or“degenerate”,Not all numbers have an inverse.,Matrix inverse:If A is an m x m matrix,and if it has an inverse,Matrices that dont have an inverse are“singular”or“degenerate”,Matrix Transpose,Example:,Let be an m x n matrix,and let Then is an n x m matrix,and,