Some special types of matrix diagonal matrix:a square matrix with zeros everywhere except possibly on the diagonal which runs from the top left to the bottom right.This diagonal is called the leading diagonal. Here are some diagonal matrices: -(6)-88 100 100 G- 00 0 001 Note:Whereas all the non-diagonal elements are zero,the elements on the leading diagonal can be any number including zero. 务这头子 Matrix Theory Matrices -4/14
Some special types of matrix ▸ diagonal matrix: a square matrix with zeros everywhere except possibly on the diagonal which runs from the top left to the bottom right. This diagonal is called the leading diagonal. Here are some diagonal matrices: E = ( 2 0 0 −5 ) F = ⎛ ⎜ ⎝ 1 0 0 0 2 0 0 0 3 ⎞ ⎟ ⎠ G = ⎛ ⎜ ⎝ 1 0 0 0 0 0 0 0 1 ⎞ ⎟ ⎠ Note: Whereas all the non-diagonal elements are zero, the elements on the leading diagonal can be any number including zero. Matrix Theory Matrices - 4/14
Some special types of matrix identity matrix (or unit matrix):a diagonal matrix with all its diagonal elements equal to 1. 命电有这女子 Matrix Theory Matrices -5/14
Some special types of matrix ▸ identity matrix (or unit matrix): a diagonal matrix with all its diagonal elements equal to 1. The following are identity matrices: ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ ( 1 0 0 1 ) ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Notes: 1. The symbol I is usually reserved for labelling identity matrices. 2. The columns of the identity matrix are also called canonical vectors ei. 3. Use a subscript to indicate the size of the particular identity matrix we are discussing. So we might write I3 = ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ I2 = ( 1 0 0 1 ) I4 = ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Matrix Theory Matrices - 5/14
Some special types of matrix identity matrix (or unit matrix):a diagonal matrix with all its diagonal elements equal to 1. The following are identity matrices: 0 00 ()(&) 00 1 1 1 命电有这女子 Matrix Theory Matrices -5/14
Some special types of matrix ▸ identity matrix (or unit matrix): a diagonal matrix with all its diagonal elements equal to 1. The following are identity matrices: ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ ( 1 0 0 1 ) ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Notes: 1. The symbol I is usually reserved for labelling identity matrices. 2. The columns of the identity matrix are also called canonical vectors ei. 3. Use a subscript to indicate the size of the particular identity matrix we are discussing. So we might write I3 = ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ I2 = ( 1 0 0 1 ) I4 = ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Matrix Theory Matrices - 5/14
Some special types of matrix identity matrix (or unit matrix):a diagonal matrix with all its diagonal elements equal to 1. The following are identity matrices: 0 0 0 ()(6) 0 00 1 0 1 Notes: 奇老有这头 Matrix Theory Matrices -5/14
Some special types of matrix ▸ identity matrix (or unit matrix): a diagonal matrix with all its diagonal elements equal to 1. The following are identity matrices: ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ ( 1 0 0 1 ) ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Notes: 1. The symbol I is usually reserved for labelling identity matrices. 2. The columns of the identity matrix are also called canonical vectors ei. 3. Use a subscript to indicate the size of the particular identity matrix we are discussing. So we might write I3 = ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ I2 = ( 1 0 0 1 ) I4 = ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Matrix Theory Matrices - 5/14
Some special types of matrix identity matrix (or unit matrix):a diagonal matrix with all its diagonal elements equal to 1. The following are identity matrices: 0 0 0 (8)() 1 0 0 0 1 0 .0 00 Notes: 1.The symbol is usually reserved for labelling identity matrices. 奇电有这头 Matrix Theory Matrices -5/14
Some special types of matrix ▸ identity matrix (or unit matrix): a diagonal matrix with all its diagonal elements equal to 1. The following are identity matrices: ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ ( 1 0 0 1 ) ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Notes: 1. The symbol I is usually reserved for labelling identity matrices. 2. The columns of the identity matrix are also called canonical vectors ei. 3. Use a subscript to indicate the size of the particular identity matrix we are discussing. So we might write I3 = ⎛ ⎜ ⎝ 1 0 0 0 1 0 0 0 1 ⎞ ⎟ ⎠ I2 = ( 1 0 0 1 ) I4 = ⎛ ⎜ ⎜ ⎜ ⎝ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ Matrix Theory Matrices - 5/14