Row-reducing Algorithms

January 4, 2008

Row reduction is the process of using row operations to transform a matrix into a row reduced echelon matrix. As the algorithm proceeds, you move in stairstep fashion through different positions in the matrix. In the description below, when I say that the current position is (i, j) , I mean that your current location is in row i and column j. The current position refers to a location, not the element at that location. The current row means the row of the matrix containing the current position.

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Row reduction

January 4, 2008

What is row reduction?

Row reduction (or Gauss-Jordan elimination) is the process of using row operations to reduce a matrix to row reduced echelon form. This procedure is used to solve systems of linear equations, invert matrices, compute determinants, and do many other things.


A matrix is in row reduced echelon form if the following conditions are satisfied:

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There are three kinds of row operations. Actually, there is some redundancy here – you can get away with two of them.

1. Swapping two rows:

Here is a swap of rows 2 and 3. I’ll denote it by $r_2 \leftrightarrow r_3$.


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Vector Space

January 4, 2008

What is Vector Space?

A vector space is a set on which two operations, called (vector) addition and (scalar) multiplication, are defined and satisfy certain natural axioms.


Formal Definition

Let F be a field (such as the real numbers or complex numbers), whose elements will be called scalars. A vector space over the field F is a set V together with two binary operations, Read the rest of this entry »

Matrix Row Operations

January 4, 2008

For matrices, there are three basic row operations. They are:

* Row switching: Interchange rows

* Row multiplication:  Multiply a row by a non-zero constant, changing that row

* Row addition: Use a pivot row to change a target row by multiplying the pivot row by a constant and adding the resulting products to the target row. The pivot row is not changed


Useful link for Matrix Row Operations:

Port numbers

January 3, 2008

The port numbers are divided into three ranges:

– The well-known ports are those in the range 0 through 1023

– The registered ports are those in the range 1024 through 49151

– The dynamic or private ports are those in the range 49152 through 65535

For the complete list of assigned port numbers from the Internet Assigned Numbers Authority (IANA), please go to: