A Geometric Review of Linear Algebra [pdf](cns.nyu.edu)

   A = UΣV^T

   A = UΛU^T

    {arithmetic}
    |
    {vecops} = {Vector operations}
    {dotproduct}

    {arithmetic}
    |
    {RREF}   = {Reduced row echelon form}

    {arithmetic}
    |  {patience}
    |  |  {dotproduct}
    |  |  |
    {matrices}
    {Mops}   = {Matrix operations}
    {Meqns}  = {Matrix equations}
    {Mmult}  = {Matrix multiplication}
    {Mdet}   = {Determinants}
    {Minv}   = {Matrix inverse}

    {y=mx+b}
    | 
    {linear} = {Linearity}
    {plane}  = {Lines and planes}

    {dotproduct}
    |
    {proj}   = {Projections}
    {basis}  = {Coordinate projections}

    {vectors}
    |
    {VS1}    = {Vector spaces}
    {VS2}    = {Abstract vector spaces}           // knowledge buzz moment
    |
    |  {dotproduct}
    |  |
    {IPS}    = {Abstract inner product spaces}

    {y=mx}
    | {Mmult}
    | |  {function  f:R->R}
    | |  |
    {linT}   = {Linear transformations}
    {VSRREF} = {Vector space techniques for matrices}
    {TasM}   = {Finding matrix representations}
    {basis2} = {Change of basis for matrices}

    {Mmult}
    |  {linT}
    |  |
    {eigV}   = {Eigenvalues and eigenvectors}
       {Mdecomp}= {Matrix decompositions}
       |
    {specM}  = {Special types of matrices}

    {VS1}
    |{plane}
    ||{eigV}
    |||{linT}
    |||||{Meqns}
    ||||||{Mmult}
    ||||||||{Mdet}
    |||||||||
    {invMthm} = {Invertible matrix theorem}          

    {proj}
     |
    {GSorth} = {Gram--Schmidt orthogonalization}

    {RREF}
    |
    {LP}     = {Linear programming}

    {Mmult}
    |{Meqn}
    ||{RREF}
    |||
    {solve}  = {Solving systems of equations}
    {LSaprx} = {Least squares approximate solution}
    {ML}     = {Machine learning}

    {LAoverZ_q}= {Linear algebra over a finite field}
    |||
    ||{ECCs}   = {Error correcting codes}
    |{crypto} = {Cryptography}
    {netcode}= {Network coding}

    {trig}
    |{taylor}
    ||{AVS}
    |||{IPS}
    |||||
    {fourier}= {Fourier series}

   {fourier}
    | {prob}   = {Probability density}
    | |  {LAoverC}= {Linear algebra with complex numbers}
    | |  |
    {quantum}= {Quantum mechanics}