[
    {
        "file_id": "d32WV1rKoVk",
        "query_id": 0,
        "timestamp": 1684518790918.0,
        "annotatedSourceSentencesIndices": [
            211
        ],
        "names": [
            "annotator1"
        ],
        "text": "so...how to find the proper \"shift\"?"
    },
    {
        "file_id": "d32WV1rKoVk",
        "query_id": 1,
        "timestamp": 1684518968338.0,
        "annotatedSourceSentencesIndices": [
            35
        ],
        "names": [
            "annotator1"
        ],
        "text": "How do we get A2 from A1 ??"
    },
    {
        "file_id": "d32WV1rKoVk",
        "query_id": 2,
        "timestamp": 1684519128837.0,
        "annotatedSourceSentencesIndices": [
            65
        ],
        "names": [
            "annotator1"
        ],
        "text": "Should we not use A0 = QR ,  A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?"
    },
    {
        "file_id": "d32WV1rKoVk",
        "query_id": 3,
        "timestamp": 1684519167076.0,
        "annotatedSourceSentencesIndices": [
            337
        ],
        "names": [
            "annotator1"
        ],
        "text": "Is he talking about Galois or Abel?"
    },
    {
        "file_id": "d32WV1rKoVk",
        "query_id": 4,
        "timestamp": 1684519760474.0,
        "annotatedSourceSentencesIndices": [
            250
        ],
        "names": [
            "annotator1"
        ],
        "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture"
    },
    {
        "file_id": "d32WV1rKoVk",
        "query_id": 6,
        "timestamp": 1684519784891.0,
        "annotatedSourceSentencesIndices": [
            250
        ],
        "names": [
            "annotator1"
        ],
        "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research.  Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a  5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues?  This doesn't sit right with me, so I'm thinking that can't be it."
    },
    {
        "file_id": "d32WV1rKoVk",
        "query_id": 7,
        "timestamp": 1684519933908.0,
        "annotatedSourceSentencesIndices": [
            211,
            214
        ],
        "names": [
            "annotator1"
        ],
        "text": "What happens when the eigenvalues are complex?  It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real."
    }
]