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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3、ningAndrew NgExampleAndrew NgDetails:m x n matrix(m rows,n columns)n x 1 matrix(n-dimensionalvector)m-dimensional vectorTo get ,multiply s row with elements of vector ,and add them up.Andrew NgExampleAndrew NgHouse sizes:Andrew NgAndrew NgLinear Algebra review(optional)Matrix-matrix multiplicationMa

4、chine LearningAndrew NgExampleAndrew NgDetails:m x n matrix(m rows,n columns)n x o matrix(n rows,o columns)m x omatrixThe column of the matrix is obtained by multiplying with the column of .(for =1,2,o)Andrew NgExampleAndrew NgHouse sizes:MatrixMatrixHave 3 competing hypotheses:1.2.3.Andrew NgAndrew

5、 NgLinear Algebra review(optional)Matrix multiplication propertiesMachine LearningAndrew NgLet and be matrices.Then in general,(not commutative.)E.g.Andrew NgLetLetComputeComputeAndrew NgIdentity MatrixFor any matrix ,Denoted (or ).Examples of identity matrices:2 x 23 x 34 x 4Andrew NgAndrew NgLinea

6、r Algebra review(optional)Inverse and transposeMachine LearningAndrew NgNot 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”Andrew NgMatrix TransposeExample:Let be an m x n matrix,and let Then is an n x m matrix,and

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