Linear algebra, Linear solvers, common operations on vectors and matrices

2.1 introduction

2.2 Multiply matrix with a vector

2.3 Insert a number at speciﬁc position in a vector or list

2.4 Insert a row into a matrix

2.5 Insert a column into a matrix

2.6 Build matrix from other matrices and vectors

2.7 Generate a random 2D matrix from uniform (0 to 1) and from normal distributions

2.8 Generate an n by m zero matrix

2.9 Rotate a matrix by 90 degrees

2.10 Generate a diagonal matrix with given values on the diagonal

2.11 Sum elements in a matrix along the diagonal

2.12 Find the product of elements in a matrix along the diagonal

2.13 Check if a Matrix is diagonal

2.14 Find all positions of elements in a Matrix that are larger than some value

2.15 Replicate a matrix

2.16 Find the location of the maximum value in a matrix

2.17 Swap 2 columns in a matrix

2.18 Join 2 matrices side-by-side and on top of each others

2.19 Copy the lower triangle to the upper triangle of a matrix to make symmetric matrix

2.20 extract values from matrix given their index

2.21 Convert N by M matrix to a row of length N M

2.22 ﬁnd rows in a matrix based on values in diﬀerent columns

2.23 Select entries in one column based on a condition in another column

2.24 Locate rows in a matrix with column being a string

2.25 Remove set of rows and columns from a matrix at once

2.26 Convert list of separated numerical numbers to strings

2.27 Obtain elements that are common to two vectors

2.28 Sort each column (on its own) in a matrix

2.29 Sort each row (on its own) in a matrix

2.30 Sort a matrix row-wise using ﬁrst column as key

2.31 Sort a matrix row-wise using non-ﬁrst column as key

2.32 Replace the ﬁrst nonzero element in each row in a matrix by some value

2.33 Perform outer product and outer sum between two vector

2.34 Find the rank and the bases of the Null space for a matrix A

2.35 Find the singular value decomposition (SVD) of a matrix

2.36 Solve \(Ax=b\)

2.37 Find all nonzero elements in a matrix

2.38 evaluate \(f(x)\) on a vector of values

2.39 generates equally spaced N points between \(x_1\) and \(x_2\)

2.40 evaluate and plot a f(x,y) on 2D grid of coordinates

2.41 Find determinant of matrix

2.42 Generate sparse matrix with n by n matrix repeated on its diagonal

2.43 Generate sparse matrix for the tridiagonal representation of second diﬀerence operator in 1D

2.44 Generate sparse matrix for the Laplacian diﬀerential operator \(\nabla ^{2}u\) for 2D grid

2.45 Generate sparse matrix for the Laplacian diﬀerential operator for 3D grid

2.46 Generate the adjugate matrix for square matrix

2.47 Multiply each column by values taken from a row

2.48 extract submatrix from a larger matrix by removing row/column

2.49 delete one row from a matrix

2.50 delete one column from a matrix

2.51 generate random matrix so that each row adds to 1

2.52 generate random matrix so that each column adds to 1

2.53 sum all rows in a matrix

2.54 sum all columns in a matrix

2.55 ﬁnd in which columns values that are not zero

2.56 How to remove values from one vector that exist in another vector

2.57 How to ﬁnd mean of equal sized segments of a vector

2.58 ﬁnd ﬁrst value in column larger than some value and cut matrix from there

2.59 make copies of each value into matrix into a larger matrix

2.60 repeat each column of matrix number of times

2.61 How to apply a function to each value in a matrix?

2.62 How to sum all numbers in a list (vector)?

2.63 How to ﬁnd maximum of each row of a matrix?

2.64 How to ﬁnd maximum of each column of a matrix?

2.65 How to add the mean of each column of a matrix from each column?

2.66 How to add the mean of each row of a matrix from each row?

2.67 Find the diﬀerent norms of a vector

2.68 Check if a matrix is Hermite

2.69 Obtain the LU decomposition of a matrix

2.70 Linear convolution of 2 sequences

2.71 Circular convolution of two sequences

2.72 Linear convolution of 2 sequences with origin at arbitrary position

2.73 Visualize a 2D matrix

2.74 Find the cross correlation between two sequences

2.75 Find orthonormal vectors that span the range of matrix A

2.76 Solve \(A x= b\) and display the solution

2.77 Determine if a set of linear equations A x= b has a solution and what type of solution

2.78 Given a set of linear equations automatically generate the matrix A and vector b and solve \(A x=b\)

2.79 Convert a matrix to row echelon form and to reduced row echelon form

2.80 Convert 2D matrix to show the location and values

2.81 Find rows in matrix with zeros in them, and then remove the zeros

2.82 How to apply a function to two lists at the same time?

2.83 How to apply a function to two lists are the same time, but with change to entries?

2.84 How to select all primes numbers from a list?

2.85 How to collect result inside a loop when number of interation is not known in advance?

2.86 How ﬂip an array around?

2.87 How to divide each element by its position in a list?

2.88 How to use GramSchmidt to ﬁnd a set of orthonomal vectors?

2.2 Multiply matrix with a vector

2.3 Insert a number at speciﬁc position in a vector or list

2.4 Insert a row into a matrix

2.5 Insert a column into a matrix

2.6 Build matrix from other matrices and vectors

2.7 Generate a random 2D matrix from uniform (0 to 1) and from normal distributions

2.8 Generate an n by m zero matrix

2.9 Rotate a matrix by 90 degrees

2.10 Generate a diagonal matrix with given values on the diagonal

2.11 Sum elements in a matrix along the diagonal

2.12 Find the product of elements in a matrix along the diagonal

2.13 Check if a Matrix is diagonal

2.14 Find all positions of elements in a Matrix that are larger than some value

2.15 Replicate a matrix

2.16 Find the location of the maximum value in a matrix

2.17 Swap 2 columns in a matrix

2.18 Join 2 matrices side-by-side and on top of each others

2.19 Copy the lower triangle to the upper triangle of a matrix to make symmetric matrix

2.20 extract values from matrix given their index

2.21 Convert N by M matrix to a row of length N M

2.22 ﬁnd rows in a matrix based on values in diﬀerent columns

2.23 Select entries in one column based on a condition in another column

2.24 Locate rows in a matrix with column being a string

2.25 Remove set of rows and columns from a matrix at once

2.26 Convert list of separated numerical numbers to strings

2.27 Obtain elements that are common to two vectors

2.28 Sort each column (on its own) in a matrix

2.29 Sort each row (on its own) in a matrix

2.30 Sort a matrix row-wise using ﬁrst column as key

2.31 Sort a matrix row-wise using non-ﬁrst column as key

2.32 Replace the ﬁrst nonzero element in each row in a matrix by some value

2.33 Perform outer product and outer sum between two vector

2.34 Find the rank and the bases of the Null space for a matrix A

2.35 Find the singular value decomposition (SVD) of a matrix

2.36 Solve \(Ax=b\)

2.37 Find all nonzero elements in a matrix

2.38 evaluate \(f(x)\) on a vector of values

2.39 generates equally spaced N points between \(x_1\) and \(x_2\)

2.40 evaluate and plot a f(x,y) on 2D grid of coordinates

2.41 Find determinant of matrix

2.42 Generate sparse matrix with n by n matrix repeated on its diagonal

2.43 Generate sparse matrix for the tridiagonal representation of second diﬀerence operator in 1D

2.44 Generate sparse matrix for the Laplacian diﬀerential operator \(\nabla ^{2}u\) for 2D grid

2.45 Generate sparse matrix for the Laplacian diﬀerential operator for 3D grid

2.46 Generate the adjugate matrix for square matrix

2.47 Multiply each column by values taken from a row

2.48 extract submatrix from a larger matrix by removing row/column

2.49 delete one row from a matrix

2.50 delete one column from a matrix

2.51 generate random matrix so that each row adds to 1

2.52 generate random matrix so that each column adds to 1

2.53 sum all rows in a matrix

2.54 sum all columns in a matrix

2.55 ﬁnd in which columns values that are not zero

2.56 How to remove values from one vector that exist in another vector

2.57 How to ﬁnd mean of equal sized segments of a vector

2.58 ﬁnd ﬁrst value in column larger than some value and cut matrix from there

2.59 make copies of each value into matrix into a larger matrix

2.60 repeat each column of matrix number of times

2.61 How to apply a function to each value in a matrix?

2.62 How to sum all numbers in a list (vector)?

2.63 How to ﬁnd maximum of each row of a matrix?

2.64 How to ﬁnd maximum of each column of a matrix?

2.65 How to add the mean of each column of a matrix from each column?

2.66 How to add the mean of each row of a matrix from each row?

2.67 Find the diﬀerent norms of a vector

2.68 Check if a matrix is Hermite

2.69 Obtain the LU decomposition of a matrix

2.70 Linear convolution of 2 sequences

2.71 Circular convolution of two sequences

2.72 Linear convolution of 2 sequences with origin at arbitrary position

2.73 Visualize a 2D matrix

2.74 Find the cross correlation between two sequences

2.75 Find orthonormal vectors that span the range of matrix A

2.76 Solve \(A x= b\) and display the solution

2.77 Determine if a set of linear equations A x= b has a solution and what type of solution

2.78 Given a set of linear equations automatically generate the matrix A and vector b and solve \(A x=b\)

2.79 Convert a matrix to row echelon form and to reduced row echelon form

2.80 Convert 2D matrix to show the location and values

2.81 Find rows in matrix with zeros in them, and then remove the zeros

2.82 How to apply a function to two lists at the same time?

2.83 How to apply a function to two lists are the same time, but with change to entries?

2.84 How to select all primes numbers from a list?

2.85 How to collect result inside a loop when number of interation is not known in advance?

2.86 How ﬂip an array around?

2.87 How to divide each element by its position in a list?

2.88 How to use GramSchmidt to ﬁnd a set of orthonomal vectors?