DAY20
Wednesday, 27 June 2012

Today we may talk about:

• how a matrix in linear algebra can be declared in C as a two-dimensional array.
• how a matrix is initialized, modified, and used.
• how a matrix is stored.
• how the sizeof() function can tell you the sizes of things (chars, ints, floats, doubles, and arrays of these things)
• how to use the VLA (variable length array) idea to create a matrix whose size is chosen by the user at run time.
• how to use scanf() to read a value directly into a particular array location.
• how a matrix can be used to store image information.
• How to compute certain matrix norms.
• How to implement matrix-vector multiplication in C.
• How to implement matrix-matrix multiplication in C.
• A formula for the inverse matrix.
• How to implement the Jacobi iteration for solving certain linear equations.
• How to implement the power method for finding the largest eigenvalue.

Programs and functions we might talk about:

• feep.ascii.pbm, a tiny black and white ASCII graphics file in Portable Bit Map (PBM) format.
• feep.png, the image stored in the graphics file.
• matrix_inverse.c, shows how the entries of a matrix can be read directly by scanf(); computes the inverse of a 2x2 matrix specified by the user.
• matrix_matrix.c, matrix-matrix multiplication example, computes C = A * B. A is a 4x3 matrix, B is a 3x2 matrix.
• matrix_vector.c, matrix-vector multiplication example, computes A*x = b.
• matrix_vla.c, shows how the VLA idea can also be used with matrices. We can let the user input the dimensions of the matrix, and then declare it.
• sizes.c, shows how the sizeof() function can be used to ask for the size (in bytes) of a datatype, a variable, or an array.