See invertible matrix on Wiktionary
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"examples": [
{
"text": "1975 [Prentice-Hall], Kenneth Hoffman, Analysis in Euclidean Space, Dover, 2007, page 65,\nIt says that, if A is a singular matrix, then every neighborhood of A contains an invertible matrix. In other words, if A is singular, we can perturb A just a little and obtain an invertible matrix."
},
{
"ref": "1997, Bernard L. Johnston, Fred Richman, Numbers and Symmetry: An Introduction to Algebra, CRC Press, page 199:",
"text": "There are certain very simple invertible matrices, and every invertible matrix over a field can be built up out of them.",
"type": "quote"
},
{
"ref": "2013, Mahya Ghandehari, Aizhan Syzdykova, Keith F. Taylor, “A four dimensional continuous wavelet transform”, in Azita Mayeli, editor, Commutative and Noncommutative Harmonic Analysis and Applications, American Mathematical Society, page 123:",
"text": "The space of real square matrices of fixed size is a vector space whose dimension is a perfect square and the invertible matrices constitute a dense open subset of this vector space.",
"type": "quote"
}
],
"glosses": [
"Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
],
"hyponyms": [
{
"word": "unitary matrix"
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"id": "en-invertible_matrix-en-noun-X~ibcDka",
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"raw_glosses": [
"(linear algebra) Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
],
"topics": [
"linear-algebra",
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"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "kääntyvä matriisi"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "invertierbare Matrix"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "reguläre Matrix"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "invertálható mátrix"
},
{
"code": "it",
"lang": "Italian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "matrice invertibile"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "seisoku gyōretsu",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "正則行列"
},
{
"code": "pl",
"lang": "Polish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
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"word": "macierz odwrotna"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "matrice inversabilă"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"common-gender"
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"word": "inverterbar matris"
}
],
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"word": "invertible matrix"
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"text": "1975 [Prentice-Hall], Kenneth Hoffman, Analysis in Euclidean Space, Dover, 2007, page 65,\nIt says that, if A is a singular matrix, then every neighborhood of A contains an invertible matrix. In other words, if A is singular, we can perturb A just a little and obtain an invertible matrix."
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"text": "There are certain very simple invertible matrices, and every invertible matrix over a field can be built up out of them.",
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{
"ref": "2013, Mahya Ghandehari, Aizhan Syzdykova, Keith F. Taylor, “A four dimensional continuous wavelet transform”, in Azita Mayeli, editor, Commutative and Noncommutative Harmonic Analysis and Applications, American Mathematical Society, page 123:",
"text": "The space of real square matrices of fixed size is a vector space whose dimension is a perfect square and the invertible matrices constitute a dense open subset of this vector space.",
"type": "quote"
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"glosses": [
"Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
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"(linear algebra) Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
],
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{
"code": "fi",
"lang": "Finnish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "kääntyvä matriisi"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "invertierbare Matrix"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "reguläre Matrix"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "invertálható mátrix"
},
{
"code": "it",
"lang": "Italian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "matrice invertibile"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "seisoku gyōretsu",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "正則行列"
},
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"code": "pl",
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"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
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"code": "ro",
"lang": "Romanian",
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"tags": [
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"word": "matrice inversabilă"
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"code": "sv",
"lang": "Swedish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
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"word": "inverterbar matris"
}
],
"word": "invertible matrix"
}
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