# Linear Algebra in Computer Science

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Linear algebra is a useful tool with many applications within the computer science field. This paper will cover the various applications of linear algebra in computer science including: internet search, graphics, speech recognition,and artificial intelligence. A major focus of linear algebra in computer science is internet searches, which involves finding techniques for effectively storing and searching through information.
In the year 2000 there was an estimated 2.5 billion web pages on the internet, with a growth rate of 7.3 million per day. Linear algebra is used in the organization and sorting of these web pages when storing them in an internet search database. The vector space model;is used to enhance search results by representing them as two vectors, the document vector and query vector. Each dimension in the vector corresponds to a different term. If the term occurs in the document, its value in the vector is a non-zero value. Several different ways of computing the term weights have been developed, one of which is the frequency-inverse document frequency (tf-idf) weights. The frequency portion if td-idf refers to the frequency of the term within the document. The inverse document frequency is the log function of the total number of documents / divided by the number of documents in which the term appears.The frequency-inverse document model just multiplies these 2 values. Using the cosine similarity between the document and query vector allows the computer to group data together or output data that is similar. The major advantages of using this model over the standard boolean model is that it allows ranking of documents according to their relevance, and it allows partial matching. There are a large number of variations of ...

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...ing in statistical machine learning are probability distributions and parameter spaces which are represented using vectors. Currently the use of linear algebra within AI’s can be avoided when using prepared libraries, but to understand how and why the algorithms work in the AI unit you will need linear algebra.
Linear algebra has a large impact on the computer science field and is one of the most important tools to learn if you are committed to excelling in computer science. Linear algebra has its effect in a large number of applications in computer science but some of the most significant impact are its use for organizing and sorting through large amounts of web pages in the internet search database, its ability to transform graphical images, it’s impact on voice recognition, and lastly its ability to provide AI with the concept of statistical machine learning.