Linear Algebra

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Linear Algebra by Mind Map: Linear Algebra

1. Week 1

1.1. the relationship between machine learning,linear algebra and vectors and matrices.

1.2. vectors in data science

2. Wee 2

2.1. vectors

2.2. finding the size of a vector,its angle and projection.

2.3. changing the reference frame

2.3.1. changing basis

2.3.2. basis,vector space and linear independce

2.3.3. application of changing basis

2.3.4. doing some real-world vectors example

3. Week 3

3.1. introduction to matrices

3.2. matrices in linear algebra:operating on vectors

3.2.1. how matrices transform space

3.2.2. types of matrix transformation

3.2.3. composition and combination of matrix transformations

3.2.4. using matrices to make transformations

3.3. matrix inverses

3.3.1. solving the apples and bananas problems:Gaussian elimination

3.3.2. going from Gaussian elimination to finding the inverse matrix

3.3.3. solving the linear equations using the inverse matrix

3.4. special matrices and coding up some matrix operations

3.4.1. determinants and inverses

3.4.2. identifying special matrices

4. Week 4

4.1. matrices as objects that map one vector onto another;all the types of matrices

4.1.1. introduction Einstein summation convention and the symmetry of the dot product

4.1.2. non-square matrix multiplication

4.2. matrices transform into the new basis vectors set

4.2.1. matrices changing basis

4.2.2. doing a transformation in a changed basis

4.2.3. mapping to spaces with different numbers of dimensions

4.3. making multiple mappings,deciding id these are reversible

4.3.1. orthogonal matrices

4.4. recognizing mapping matrices and applying these to data

4.4.1. the Gram-Schmidt process

4.4.2. example:reflecting in a plane

4.4.3. reflecting Bear

5. Week 5

5.1. what are eigen-things?

5.1.1. what are eigenvalues and eigenvectors?

5.1.2. selecting eigenvectors by inspection

5.2. getting into the detail of eigenprolems

5.2.1. special eigen-cases

5.2.2. calculating eigenvectors

5.2.3. characteristic polynomials,eigenvalues and eigenvectors

5.3. when changing to the eigenbasis is really useful

5.3.1. changing to the eigenbasis

5.3.2. eigenbasis example

5.3.3. diagonalisation and applications

5.4. making the PageRank algorithm