Last updated April 10, 2022

Status: Tags: #cards/math232/unit3 Links: MATH 232 Units

Matrix

Principles

• Element in matrix is called ;; entries

Syntax (size, specific element) ?

• Denote size by $A_{mxn}$
• Denote specific element by $[aij]{mxn}$ or $[aij]$ or $(A){ij}$

• Matrix Operations

• Matrix Vector Multiplication

• Matrices can scale, reflect, rotate

• Some matrices are length preserving

• m=n

• when i=j then it is a diagonal entry

Diagonal matrix ?

• a square matrix where non-diagonal entries are all 0

Identity Matrix ?

• when all diagonal entries are 1
• Resembles 1 of matrixes
• multiplicative identity element (nothing happens when we multiply with another matrix)
• Always square
• Diagonal, UT, LT
• Column vectors and row vectors and standard basis vectors for R^n where n is columns

Triangular matrix ?

• Upper triangular or lower triangular

  • A is UT if aij = 0 for every i>j
  • A is LT if aij = 0 for every j>ix

• Standard Matrix

Decomposition into vectors

?

• Matrix can be turned into a row list of columnar vectors or
  • each column is vector
• a columnar list of row vectors
  • each row is vector
• 

Characteristics

• Matrix Span
• Matrix linear independence
• Matrix Transpose
• Matrix Linearity Properties
• Matrix Mapping

Examples

Backlinks

1

list from Matrix AND !outgoing(Matrix)

References:

Created:: 2022-01-25 19:57