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* * * *
0 * * *
0 0 * *
0 0 0 *
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| the product of two upper triangular matrices is |
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Definition
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1 * * *
0 1 * *
0 0 1 *
0 0 0 1
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Definition
unit upper triangular matrix
(notation for all flash cards: * represents any number) |
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| the product of two unit upper triangular matrices is |
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Definition
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| the product of an upper Hessenberg and an upper triangular matrix is |
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Definition
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* * * *
* * * *
0 * * *
0 0 * *
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Definition
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* 0 0 0
0 * 0 0
0 0 * 0
0 0 0 *
only the main diagonal of the matrix is nonzero |
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Definition
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| If A is diagonal, the product SA does what? |
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Definition
| scales the columns of S by the elements on the main diagonal of A |
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| If A is diagonal, the product AS does what? |
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Definition
| scales the rows of S by the diagonal elements of A |
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Definition
a matrix in which each descending diagonal from left to right is constant
a b c d
e a b c
f e a b
g f e a
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| Draw a columnwise interpretation of a matrix times a vector. |
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Definition
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Definition
| The i'th column of a matrix A |
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* * 0 0
* * * 0
0 * * *
0 0 * *
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Definition
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Definition
exchanging, multiplying, and adding rows of a matrix to each other to get a triangular matrix
(main diagonal should end up nonzero if you expect to find one solution) |
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Definition
| scale and recombine rows until you have the identity matrix |
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Definition
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Definition
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Definition
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Definition
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| number of rows (height of matrix) |
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| number of columns (width of matrix) |
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Definition
4 2 0 2
6 3 0 3
2 1 0 1
8 4 0 4
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Definition
| A = V A0 VH, where V is unitary and A0 is Hessenberg |
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| A unitary matrix and satisfies the condition that |
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Definition
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| The hermitian transpose is another name for the conjugate transpose. |
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