_index.md (3681B)
1 +++ 2 title = 'Linear Algebra' 3 +++ 4 5 # Linear Algebra 6 If you need help with any of the topics, check out [PatrickJMT on Youtube](https://www.youtube.com/user/patrickJMT). He has some of the best math videos on the internet. 7 8 [Preliminary - a great article about why linear algebra is useful and important.](intuitive-guide-to-linear-algebra-notes/) 9 10 - [Introduction](introduction) 11 - [Linear Equations](introduction#linear-equations) 12 - [Matrix notation](introduction#matrix-notation) 13 - [Reducing a matrix](introduction#reducing-a-matrix) 14 - [Vectors](introduction#vectors) 15 - [Solution sets of linear systems](solution-sets-of-linear-systems) 16 - [Homogeneous linear systems](solution-sets-of-linear-systems#homogeneous-linear-systems) 17 - [Parametric vector form](solution-sets-of-linear-systems#parametric-vector-form) 18 - [Linear independence](solution-sets-of-linear-systems#linear-independence) 19 - [Linear transformations](linear-transformations) 20 - [Matrix operations](matrix-operations) 21 - [Sums and scalar multiples](matrix-operations#sums-and-scalar-multiples) 22 - [Powers of a matrix](matrix-operations#powers-of-a-matrix) 23 - [Transpose of a matrix](matrix-operations#transpose-of-a-matrix) 24 - [Inverse of a matrix](matrix-operations#inverse-of-a-matrix) 25 - [Elementary matrices](matrix-operations#elementary-matrices) 26 - [Applications to computer graphics](applications-to-computer-graphics) 27 - [Homogeneous coordinates](applications-to-computer-graphics#homogeneous-coordinates) 28 - [2D](applications-to-computer-graphics#2d) 29 - [3D](applications-to-computer-graphics#3d) 30 - [Composite transformations](applications-to-computer-graphics#composite-transformations) 31 - [Perspective projections](applications-to-computer-graphics#perspective-projections) 32 - [Vector spaces](vector-spaces) 33 - [Column space and null space of a matrix](vector-spaces#column-space-and-null-space-of-a-matrix) 34 - [Basis for a subspace](vector-spaces#basis-for-a-subspace) 35 - [Coordinates](vector-spaces#coordinates) 36 - [Dimension of a subspace](vector-spaces#dimension-of-a-subspace) 37 - [Eigenvectors & eigenvalues](eigenvectors-eigenvalues) 38 - [Determinant](eigenvectors-eigenvalues#determinant) 39 - [Similarity](eigenvectors-eigenvalues#similarity) 40 - [Diagonalization](eigenvectors-eigenvalues#diagonalization) 41 - [Orthogonality & least squares](orthogonality-least-squares) 42 - [Inner (dot) product & uses](orthogonality-least-squares#inner-dot-product-uses) 43 - [Length of a vector](orthogonality-least-squares#length-of-a-vector) 44 - [Distance between vectors](orthogonality-least-squares#distance-between-vectors) 45 - [Orthogonal complement](orthogonality-least-squares#orthogonal-complement) 46 - [Orthogonal sets](orthogonality-least-squares#orthogonal-sets) 47 - [Orthogonal projections](orthogonality-least-squares#orthogonal-projections) 48 - [Orthogonal decomposition](orthogonality-least-squares#orthogonal-decomposition) 49 - [Best approximation](orthogonality-least-squares#best-approximation) 50 - [When basis for W is an orthonormal set](orthogonality-least-squares#when-basis-for-w-is-an-orthonormal-set) 51 - [Gram-Schmidt process](orthogonality-least-squares#gram-schmidt-process) 52 - [QR factorization](orthogonality-least-squares#qr-factorization) 53 - [Least-squares problems](orthogonality-least-squares#least-squares-problems) 54 - [Symmetric matrices](symmetric-matrices) 55 - [Diagonalization of symmetric matrices](symmetric-matrices#diagonalization-of-symmetric-matrices) 56 - [Singular value decomposition](symmetric-matrices#singular-value-decomposition)