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given that v and w are in the subspace,
i) v + w is in the subspace
ii) cv is in the subspace |
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| Vectors comprising a subspace |
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| number of vectors in basis |
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| Project line b onto line a |
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x_hat = a.b/a.a
p = x_hat * a |
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| Projecting onto subspace A |
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p = A * x_hat
A^T * A * x_hat = A^T * b |
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| I (product of orthonormal columns and transpose) |
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| Vn = v - V1.v/V1.V1 * V1 - .... |
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| R = {{q1.a , q1.b , q1.c},{0 , q2.b , q2.c}.... |
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| If two rows are swapped in A, what happens to Det(A)? |
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| determinant multiplied by constant, what happened inside matrix? |
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| top row multiplied by constant |
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| can split determinant into two if... |
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| only top row is split into two |
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| T/F, the determinant stays the same if two rows are added/subtracted? |
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| T/F, the determinant stays the same if two rows are multiplied? |
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| Easy way to find determinant in triangular matrix... |
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| Product of diagonal entries |
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| cofactor expansion. Det(A) = .... |
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| a_11 * c_11 + a_12 * c_12 ..... |
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Solves Ax = b
x_1 = det(B_1)/det(A) ... |
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| Inverse A^-1 using cofactors |
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| Area of triangle with points (x1,y1), (x2,y2), (x3,y3) |
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| 1/2 { x ... y .... 1... } |
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| Triple Product = (u x v).w = {{ w } { u } { v }} = {{ u } { v } { w }} |
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| If every col adds to 1 in matrix, an eiganvalue is.... |
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| if A is singular, and eiganvalue is... |
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| if A is symetric, all eiganvectors are.... |
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| T/F, does elimination preserve eiganvalues? |
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| Product of eiganvalues = .... |
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| Solution for u_(k+1) = A * u_k |
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c1*(lambda1)^k * x1 ...
where C = S^-1 * u_0 |
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| T/F. All symmetric matrices are diagonalizable? |
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| T/F, Symmetric matrices have only real eigenvalues |
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| T/F, Symmetric matrices have orthogonal eigenvectors |
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| Symmetric matrices with only positive eiganvalues |
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| A is similar to B = M^-1 * A * M |
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| What do similar matrices share in common? |
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| Eigenvalues, trace, determinant, rank, and number of independent eigenvectors |
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