Basic Linear Algebra in R by Ankita Jain

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Basic Linear Algebra in Rby Ankita Jain
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Vectors

• Defining a column vector
• Transpose of a vector
• Addition of two vectors
• Multiplication of a vector with a scalar and
  another vector
• Inner Product of vectors ( a is orthogonal to c
  iff a.c0)
• Length(norm ) of a vector

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Matrices

• Defining a matrix with first argument as array of
  numbers and second specifying number of columns
• By default numbers are put column wise in matrix.
  byrowT makes it put row wise in matrix.
• Adding two matrices(similarly for vectors)
• Trace of a matrix t(B)
• Multiplication of Matrix with a scalar and with
  a matrix (similarly with a vector)

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Matrices

• Diagonal of a matrix
• Defining a diagonal matrix
• Inverse of a matrix solve(A)
• To solve Axb, we find xA-1B (Binv(A), x Bb)

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Other Matrix Operations

• Finding determinant of a matrix
• eigen(A) Eigen values and vectors of a matrix
• cbind(A,B) Concatenating two matrices
• Row Operations in a matrix
• Multiply a row by a (non-zero) constant
• Multiply a row by a non-zero constant and add the
  result to another row
• Interchange two rows

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Reading Data from a File

• Scan command loads the file in R
• Selecting particular rows and columns from the
  scanned file