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Linear Algebra

Decomposition

LU

is a lower triangular matrix

is an upper triangular matrix

 > LU

QR

is an orthgonal matrix of size

is an upper triangular matrix of size

 > QR

Rank

is an

matrix

is an

matrix

is the rank of

 > Rank

Singular Value

latex!encoded:base64,QT1VRFZee0h9
latex!encoded:base64,RA==

is a nonnegative diagonal matrix

latex!encoded:base64,VQ==

and

latex!encoded:base64,Vg==

are unitary matrices

latex!encoded:base64,Vl57SH0=

is the conjugate transpose of

(transpose if

contains reals only)

 > Singular Value

Eigendecomposition

is a diagonal matrix formed from the eigenvalues of

The columns of

are the eigenvectors of

 > Eigendecomposition
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