Errata for "Totally Nonnegative Matrices"

Working Errata list (last updated: May 22, 2012)

**page 3, lines 5,6: "...the positive diagonal matrices (D_n) are also InTN."
**page 5, line 5: (a_i \geq 0, b_i, c_i >0)
**page 5, line 9: A[{1,2,4,6,7}] --> A[{1,2,4,6,7,8}]
**page 6, line 7: and --> and/or
**page 7, line -9: eigenvalues of an irreducible normal Jacobi matrix...
**page 7, line -6: |b_{i}| + |c_{i}| --> |b_{i}| + |c_{i-1}|

**page 8, in the displayed matrix the (n,n) entry should be a_{n} not a_{n-1}

**page 9, line 2: D_{k}D_{k-1} --> D_{k-1}D_{k+1}
**page 9, line -1: "nonnegative tridiagonal P_0 matrices arem in fact, TN."
**page 10, line 4: 'entrywise nonnegative, irreducible, and invertible P_0 tridiagonal..."
**page 10, line 13: [min{i,j}] matrix: \cdots instead of \cdot
**page 12, line 1: V(x_1,x_2,\cdots < x_n) --> V(x_1,x_2, \ldots, x_n)

**page 12, line 11: 0< x_1 < x_2 < x_3 --> 0 < x_1 < x_2 < \cdots < x_n

**page 14, line 3: "...from f is TN and invertible
**page 15, A sequence of real numbers is called totally positive if the displayed two-way infinite matrix is "TN".
**page 15, An infinite matrix is called "TN" if all of its minors are "nonnegative".

**page 18, line 7: in displayed matrix n should be replaced by p
**page 18, line 8: \Delta_{p}(X) \times \Delta(Y) --> \Delta_{p}(X) \times \Delta_{p}(Y)
**page 21, line 18: in displayed equation $\alpha_1 --> \alpha_{i}
**page 30, (1.6): insert a + sign in the second line to read as:

det A({a,b},{1,q})det A({a},{n}) + det A({a,b},{q,n})det A({a},{1})
**page 32, lines -12,-13: add two ], to read as "... = det A[{1,2,4,5},{1,2,4,5}]det A[{2,5},{2,4}] + det A[{1,2,5},{2,4,5}] det A[{2,4,5},{1,2,4}].
**page 32, line -7: insert a + sign in this line to read as:

det A({a,b},{1,q})det A({a},{n}) + det A({a,b},{q,n})det A({a},{1})
**page 33, line -13: change "only one" to "at most one"
**page 39, lines 5, 6: "size" means sum of rows and columns
**page 47, (2.2) -- > L_{4}(\cdot)L_{3}(\cdot)L_{2}(\cdot)L_{4}(\cdot)L_{3}(\cdot)L_{4}(\cdot)D

U_{4}(\cdot)U_{3}(\cdot)U_{4}(\cdot)U_{2}(\cdot)U_{3}(\cdot)U_{4}(\cdot)
**page 49, line 10: - a_{1,j+1}/a_{1j} --> - a_{j+1,1}/a{j1}
**page 49, (2.6): a_{1, j+1} --> a_{j+1,1} and a_{1j} --> a_{j1}
**page 49, line -5: , a_{s1} --> , a_{s-1,1}
**page 50, line 10: det A'[x \cup \alpha, 2 \cup \beta] --> det A'[y \cup \alpha, 2 \cup \beta]
**page 50, lines 11 & 16: in displayed equations: \times --> -
**page 58, line 2: j \leq 1 --> j \geq 1
**page 64, Lindstr\ddot{o}m --> Lindstr\"om

**page 75, line 14: first displayed matrix after "=" replace a_{12} by a_{21}
**page 76, line 14: switch "sink" and "source"
**page 79, line -17: n-m --> n-m+2 & n-m+1 --> n-m+2
**page 81, line -2: M --> G
**page 84, line 6: (display) 0 \leq det L [ \gamma \cup \alpha, \gamma \cup \beta]
**page 93, line 16: "Then the m-by-n matrix A'..." --> "Then the m-by-n' matrix A'..."
**page 93, line -7: "...column compression A of A'..." --> "...column compression A' of A..."
**page 94, line 2: $x_1, x_2, \ldots, x_{k_1}$ --> $x'_1, x'_2, \ldots, x'_{n'}$
**page 100, line -4: "...are a right eigenvector...: --> "...is a right eigenvector..."
**page 102, line -9: "...and $u^(1)$ and $w^{n)$ ($w^(1) w^(n)$)..." --> "...and $u^(1)$ and $u^{n)$ ($w^(1), w^(n)$)..."
**page 111, line -20: (n, rank(A), p - rank(A)) --> (n, rank(A), p-rank(A))
**page 113, lines -1 -3: a_{21} --> a_{21}^T
**page 119, Theorem 5.5.2: Technically it should read that the eigenvalues of $A(1)$ or $A(n)$ interlace the eigenvalues of $A$.
**page 127, line 11: are --> is
**page 130, (6.5): det A[U,V] det A[V,U] \geq 0
**page 130, line 19: "...index sets $S,T \subseteq N$" --> "...index sets $U,V \subseteq N$"
**page 132, line 14: TN --> InTN
**page 132, line -3: should read (cf. (6.5)).
**page 137, line 8: n should replaced by infinity (\infty)
**page 137, line 11: in the displayed equation, \geq should be replaced by \leq
**page 137, (6.7): =|{ m_{js} \in M_j : m_{js} \geq k }|
**page 160, line 8: "..., then the rank of at least one of its shadows..."
**page 160, line -9 (display): k-1 --> k=1
**page 171, line 20: det([A' \circ B', t(x' \circ z')]) + det([A' \circ B', (1-t)(y' \circ z')])
**page 179, line -4: "...if A is TN_{3} (TP_{3}), then A^{(t)} is TN_{3} (TP_{3})..."
**page 180, line 15 (display) (ad-bb)(a-1) --> (ad-bc)(a-1).
**page 186, line 1: northwes --> northwest
**page 192, Theorem 9.3.1: In the TN case, we need to assume nonzero specified entries or that the partial matrix is in double echelon form.
**page 196, line -13: x<1 --> x<10
**page 212, line -6: "...if A(t) is an m-by-n TP polynomial matrix, a polynomial..."
**page 214, Lemma 10.4.1: For definition of this partial order, refer to Section 5.5.3.
**page 222, Reference [DJK08]: Korschel --> Kroschel