Linear Algebra

• matrix
  

This is a matrix ()

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• vector : an matrix
  

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• matrix addition

• Just sum the number in the same position in matrix
• only two matrix with same dimension can be added together
  

• Scalar multiplication

• take the all elements in matrix to multiple by the scalar
  

• Matrix - vector multiplication

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• A neat trick

if we know the relationship of the price and the size of the house:

• House size():
• prediction datamatrix parameters
  

• Matrix - matrix multiplication

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• Matrix multiplication properties

1. Let A and B be matrixes, then in general:

2.

• Identity matrix ( or )

%This is a 33 identity matrix

• Matrix inverse and transpose

1.matrix inverse (the matrix must be square matrix)

• if A is an matrix, and if A has an inverse:

• if all element in matrix is zero, the matrix will not have an inverse matrix

2. matrix transpose

if is a matrix, and , then