ApplyOverMatrix (a,func)
Apply a function over all entries of a matrix and return a matrix of the results
ApplyOverMatrix2 (a,b,func)
Apply a function over all entries of 2 matrices (or 1 value and 1 matrix) and return a matrix of the results
ColumnsOf (M)
Gets the columns of a matrix as a horizontal vector
ComplementSubmatrix (m,r,c)
Remove column(s) and row(s) from a matrix
CompoundMatrix (k,A)
Calculate the kth compund matrix of A
CountZeroColumns (M)
Count the number of zero columns in a matrix. For example Once you column reduce a matrix you can use this to find the nullity. See cref and Nullity.
DeleteColumn (M,col)
Delete a column of a matrix
DeleteRow (M,row)
Delete a row of a matrix
DiagonalOf (M)
Gets the diagonal entries of a matrix as a horizontal vector
DotProduct (u,v)
Get the dot product of two vectors. The vectors must be of the same size. No conjugates are taken so this is a bilinear form even if working over the complex numbers.
See Planetmath for more information.
ExpandMatrix (M)
Expands a matrix just like we do on unquoted matrix input. That is we expand any internal matrices as blocks. This is a way to construct matrices out of smaller ones and this is normally done automatically on input unless the matrix is quoted.
HermitianProduct (u,v)
Aliases: InnerProduct
Get the hermitian product of two vectors. The vectors must be of the same size. This is a sesquilinear form using the identity matrix.
See Mathworld for more information.
I (n)
Aliases: eye
Return an identity matrix of a given size, that is n by n.
See Planetmath for more information.
IndexComplement (vec,msize)
Return the index complement of a vector of indexes
IsDiagonal (M)
Is a matrix diagonal
See Planetmath for more information.
IsLowerTriangular (M)
Is a matrix lower triangular
IsMatrixInteger (M)
Check if a matrix is an integer (non-complex) matrix
IsMatrixRational (M)
Check if a matrix is a rational (non-complex) matrix
IsMatrixReal (M)
Check if a matrix is a real (non-complex) matrix
IsMatrixSquare (M)
Check if a matrix is square, that is its width is equal to its height.
IsUpperTriangular (M)
Is a matrix upper triangular
IsValueOnly (M)
Check if a matrix is a matrix of numbers
IsVector (v)
Is argument a horizontal or a vertical vector. Genius does not distinguish between a matrix and a vector and a vector is just a 1 by n or n by 1 matrix.
LowerTriangular (M)
Zero out entries above the diagonal
MakeDiagonal (v,arg...)
Aliases: diag
Make diagonal matrix from a vector
See Planetmath for more information.
MakeDiagonal (A)
Make column vector out of matrix by putting columns above each other. Returns null when given null.
MatrixProduct (a)
Calculate the product of all elements in a matrix. That is we multiply all the elements and return a number that is the product of all the elements.
MatrixSum (a)
Calculate the sum of all elements in a matrix. That is we add all the elements and return a number that is the sum of all the elements.
MatrixSumSquares (a)
Calculate the sum of squares of all elements in a matrix.
OuterProduct (u,v)
Get the outer product of two vectors
ReverseVector (v)
Reverse elements in a vector
RowSum (m)
Calculate sum of each row in a matrix
RowSumSquares (m)
Calculate sum of squares of each row in a matrix
RowsOf (M)
Gets the rows of a matrix as a vertical vector
SetMatrixSize (M,rows,columns)
Make new matrix of given size from old one. That is, a new matrix will be returned to which the old one is copied. Entries that don't fit are clipped and extra space is filled with zeros.
SortVector (v)
Sort vector elements in an increasing order.
StripZeroColumns (M)
Removes any all-zero columns of M.
StripZeroRows (M)
Removes any all-zero rows of M.
Submatrix (m,r,c)
Return column(s) and row(s) from a matrix
SwapRows (m,row1,row2)
Swap two rows in a matrix
UpperTriangular (M)
Zero out entries below the diagonal
columns (M)
Get the number of columns of a matrix
elements (M)
Get the number of elements of a matrix
ones (rows,columns...)
Make an matrix of all ones (or a row vector)
rows (M)
Get the number of rows of a matrix
zeros (rows,columns...)
Make an matrix of all zeros (or a row vector)