HP Prime Graphing Wireless Calculator Instrukcja Użytkownika Pobierz pdf (Strona 587)

100

101

Smith

Smith normal form of a matrix with coeicients in Z: returns U,B,V such that U and V invertible in Z, B is

diagonal, B[i,i] divides B[i+1,i+1], and B=U*A*V.

ismith(Mtrx(A))

Example:

ismith returns

Factorize

LQ Factorization. Factorizes a m × n matrix into three matrices L, Q, and P, where {[L[m × n lowertrapezoidal]],

[Q[n × n orthogonal]],[P[m × m permutation]]}, and P*A=L*Q.

LQ(matrix)

Examples:

LQ returns

LSQ

Least Squares. Displays the minimum norm least squares matrix (or vector) corresponding to the system

matrix1*X=matrix2.

LSQ(matrix1, matrix2)

Example:

LSQ returns

LU Decomposition. Factorizes a square matrix into three matrices L, U, and P, where {[L[lowertriangular]],

[U[uppertriangular]],[P[permutation]] }} and P*A=L*U.

LU(matrix)

Example:

LU returns

QR Factorization. Factorizes an m×n matrix A numerically as Q*R, where Q is an orthogonal matrix and R is an

upper triangular matrix, and returns R. R is stored in var2 and Q=A*inv(R) is stored in var1.

QR(matrix A,var1,var2)

Example:

Matrix functions 539

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