ueigVl [Action][Matrix][Calculation][eigVl]

Function: Returns a list that contains the eigenvalue(s) of a square matrix.

Syntax: eigVl (Mat [ ) ]

Example: To obtain the eigenvalue(s) of the matrix [[3, 4] [1, 3]]

ueigVc [Action][Matrix][Calculation][eigVc]

Function: Returns a matrix in which each column represents an eigenvector of a square matrix.

•Since an eigenvector usually cannot be determined uniquely, it is standardized as follows to its norm, which is 1:

When V = [x1, x2, ..., xn], (⎥ x1⎥ 2 + ⎥ x2⎥ 2 + .... + ⎥ xn⎥ 2 ) = 1.

Syntax: eigVc (Mat [ ) ]

Example: To obtain the eigenvector(s) of the matrix [[3, 4] [1, 3]]

uLU [Action][Matrix][Calculation][LU]

Function: Returns the LU decomposition of a square matrix.

Syntax: LU (Mat, lVariableMem, uVariableMem [ ) ]

Example: To obtain the LU decomposition of the matrix [[1, 2, 3] [4, 5, 6] [7, 8, 9]]

•The lower matrix is assigned to the first variable L, while the upper matrix is assigned to the second variable U.

To display the lower matrix

To display the upper matrix

LwUw

uQR [Action][Matrix][Calculation][QR]

Function: Returns the QR decomposition of a square matrix.

Syntax: QR (Mat, qVariableMem, rVariableMem [ ) ]

Example: To obtain the QR decomposition of the matrix [[1, 2] [3, 4]]

•The unitary matrix is assigned to variable Q, while the upper triangular matrix is assigned to variable R.

To display the unitary matrix

To display the upper triangular matrix

QwRw

uswap [Action][Matrix][Row&Column][swap]

Function: Swaps two rows of a matrix.

Syntax: swap (Mat, row number-1, row number-2 [ ) ]

Example: To swap row 1 with row 2 of the matrix [[1, 2] [3, 4]]

Chapter 2: Main Application

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